Eigen

Hold on. You emailed someone and asked them to read your proposal. I'm going to venture a guess that they weren't sitting breathless by their computer just waiting for you to email; they might have actually already had plans for how they were going to spend their time this week, possibly even next. If you're in the US, the semester is wrapping up. They probably have other students, publications to work on, and many other demands on their time that are already in place. I think it's totally reasonable for them to take a week to read your proposal. This seems like an over-reaction, or unreasonable expectations for what you should get from your advisors and on what timeline. 

I highly doubt STI set up a sock account on this forum. 

I highly doubt STI set up a sock account on this forum. 

TheAbsurdLife,
So sorry you are having to deal with these awful comments of other posters, I guess your username explains it though... you do have an absurd life!! Just ignore Fuzzy and Disco, they clearly are either 1) bored and procrastinating or 2) needing something to take their frustration out on. This forum is to ask questions, to vent, to rant, and to help us. And that's exactly what you did! You did nothing wrong. So again, I'm sorry these clearly unhappy viewers decided to lash out at you and take our their frustration. Great job not feeding into it too much! Let the unhappy just be unhappy, no need to feed them
Anywho, as of your sticky situation, I'm torn as of what to tell you. Only you can really make that call. IMO, it would definitely burn bridges... but as the other antagonistic replies have stated, that may be a bridge that's worth burning. I'm not too aware of how the funding, etc would be affected for other candidates. Do you have any sort of mentor or adviser guiding you through the application process? A professional in your field that wrote your letter of recommendation perhaps? I have had a couple questions regarding things as such, and my lovely adviser who has helped me through this whole process was willing to help me through them. Let us know (actually... forget Fuzzy and Disco... let ME know...) how everything turns out. Rooting for you!

This.
It's not very scientific to say "anyone with experience knows this to be true". Especially when there are studies (such as those linked by @TakeruK that show results the opposite of "common knowledge". 
I certainly haven't seen the biases you're talking about (male candidates being less likely to get in), unless math is strangely different than other closely related STEM fields. That said, my colleagues in math don't seem to feel like this is the case- in fact, conversations with them would assert the opposite- that male students have a better chance. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I never said there was such. There are male dominated professions and woman dominated professions however.
This is simply not true. Please link to the scientific evidence behind this.
Environmental factors may account for a portion of the variance in profession choice, but not even close to all. We know that baby infant males and females have demonstrably different preferences and behavior traits prior to environmental factors, so your theory is false. 
Science also shows us that male and female brains are quite different from each other. Differing levels of testosterone in the womb leads to divergent brain chemistry and development in males and females before birth. 
Lastly, competition and cooperation are not zero-sum. Environments need to have both - and the levels of each is debatable - to achieve optimal outcomes. More cooperation does not necessarily mean more success.
They do not necessarily change to whomever is in charge, where's the evidence for that? Institutional behavior can persist long after the removal or turnover of leaders or members. 
I also linked a study that was done where it showed that woman were given preference in job applications based on their name being on the CV. When names were removed entirely form the CVs, men were favored. I also linked to a comprehensive and methodologically deep study that showed that women were favored in STEM job hiring by approximately 33%. That was completely ignored of course, but whatever.
I am not part of the problem for 'denying your experiences' whatever that means. You are part of the problem for spreading false, and in many cases completely ideological (not factual), information. 

There's no such thing as "male" and "female" professions. Women are pushed to professions such as nursing and teaching because as infants we are conditioned to be "motherly and caring", while men are conditioned to be aggressive and build stuff. Men are not gifted with special math brains, they just grow up being more exposed to logic-based games and such. Also, competition over cooperation in science (and in most places) is bad for everyone.
Work environments are dynamic, but they change according to the views of whomever is in charge. The system has evolved organically to favor men because men have always been in charge of these fields.
Regarding your comment about men not being regarded with more respect, it is not true. Various studies have shown (some were posted here if I'm not mistaken) that men get more credibility than equally qualified women. You may not notice because you are a man and are blind to the microaggressions women in academia suffer in their everyday lives, but please stop denying our experiences, you're part of the problem.

I think calling those things "masculine qualities" is right at the root of the issues. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I have a beginning of the semester survey where I ask students to tell me about themselves, and one of the questions I ask is what they'd like me to call them. Sometimes it's a case like this, sometimes it's a "Thomas" who'd much prefer to be called Tom. 
Along with asking preferred pronouns, it's a space for students to tell me what they would prefer, and then I go by that. 

I think calling those things "masculine qualities" is right at the root of the issues. 

I think calling those things "masculine qualities" is right at the root of the issues. 

Well, if the prof made the offer then the prof gets to choose when the deadline is. The prof could have chose any deadline they wanted. 
Just to be clear, the April 15 convention is just a guidelines/agreement between all grad departments to make offers that have deadlines no earlier than April 15. So first, there is no requirement and despite what the convention says, the actual deadline on any offer is what the offer letter states (i.e. the convention is an agreement between grad schools, it has nothing to do with any individual offer) and second, after April 15, the convention does not suggest any sort of coordination between schools.

I like this one. Succinctly sums up what most of the posting here is all about. And warns new people what they're getting into. 

It fits quite well with the coffee theme of the board, and the all hours discussion. A slogan is a motto, not something that's supposed to explain a purpose.
That said, why does it need to clarify the purpose of the site? It's not like there are problems with getting new members, or with people not understanding the purpose of the site. 

Yes, if you’re enrolled. Have the option to start summer or fall, and all your subsequent years follow that start/end date. 

I think also perhaps you should have posted a much more specific thread about math, rather than "sciences" in general, since you don't really seem to want to talk about the other fields and are focused on math being so very different. 

I think you're overestimating what an email can do. 
For the first part of this, why do you want to introduce yourself? What's the benefit? Lots of people think this way, but an email introduction is next to worthless for anything practical, especially when PIs like this are probably getting a handful of unsolicited introductions a day this time of year.
For the second part- projects change. There's just as much of a chance that you'll love what your PI is working on when you start, and you have to switch projects a year in. You don't pick projects, you pick a PI. And then work on varied things. When you're a PI, you get to pick projects- until then it's all just gaining skills. And you don't know how many other people your year are going to want to work on the same thing. You're expending a lot of effort for something with marginal (if any) real benefit. 
For the final part- again, emails don't create relationships, and there's only a small chance that they can advocate for you. The worry here isn't that they'll just say "email me when you get accepted", it's that what you're doing now has the potential, if done wrong, to create a negative association. It's not likely, but it's a non-zero chance.