dualcolor

Because I got assigned to the same projects as him and now I have to carry most of the weight -.-. In addition, it wasn't just me. Some of my peers (upper-class) in my division also agreed that most of the people from the division he's in are very incompetent (i.e. lack of critical thinking skills, creativity) which could make the program, as a whole, and the school look real bad.

I got admitted for a Master's then found out people with lower stats than me got into the PhD program. To say the least, I am switching schools. Admissions is very complicated and makes no sense. My divison had no PhD spots open, but the others had lots.

I assumed the person had a comparable background as me since 2012, I did not know about his stats until recently. I started having a doubt about his credentials about six months ago because of his poor performance (Q&As) during group meetings and working on the same group project for a class. My PI has assigned 2 undergrads to him/her to help his/her project progress faster, but both of them quit after about 2 weeks. Yes, I agreed that he/she is a hard worker but that is expected for all grad students. His/her research committee decided to make him/her to give his/her research proposal a semester early for some reasons, whereas my other colleagues and I were given roughly 12 months to prepare for it.

There are, as have been said, a lot of reasons why this might be the case. 
 
Stats are a very small part of the process. Maybe those people with lower stats had stellar recommendations, did better on interviews, or really fit with a PI that sponsored them. 

That's not necessarily a good thing. 
Of course you want to get the project moving...but you will also look bad in the eyes of your PI if you aren't seen to "work well with others", or come across as arrogant & aloof towards fellow group members.
 
Nor is it necessarily fair to say that somebody would be best suited to a lab technician role, when it doesn't sound like they've been given much of a shot at independent "legitimate" research. 
 
It takes more than 1 or 2 brainstorming sessions to turn someone into an independent scientist. You might have to take a step down and say "We are going to vary X, Y, Z variables because ___. Then to make a good publication we need to prove that __ happens. Here are some good reviews on the area we're looking at." Then delegate work so you aren't dominating the project. Respect their input and ideas, even if their first "interpretations" are way off base, be polite in explaining why to encourage them to keep contributing intellectually. 
 
I don't see why this has to be a disaster, just because their stats aren't as good as yours.

Getting admitted is only a small part of the PhD. 
 
It won't damage the school's rep unless the faculty actually feel some obligation to graduate him/her with a PhD with sub-par work. 
 
It's also possible if they applied yet that your school had openings/funding and didn't have enough people on the waitlist late season. It happens. 
 
Or, as has been mentioned, there's something else about him/her that makes them a good candidate that doesn't show up in "scores". 

My PI is fully aware that I have a very strong personality (the pre-med gunner mentality), and I will most likely take over the whole project myself. The problem is that I have tried to get my colleague to participate in designing experiments which could lead to a paper, brainstorming for new ideas and novel techniques and assays etc. So far, it hasn't worked out as I wanted. I think he/she could be an excellent lab technician but doesn't have "it" to become a legit, whole-package researcher.

I wouldn't worry about the reputation of your school - I'm sure it can take care of itself. 
 
Talk to the individual and make your expectations clear for working jointly on projects. Help him out by discussing strategies for thinking critically about problems (treat somebody like a lost cause...and they usually end up acting like a lost cause) - everybody had to start from scratch at some point. If he's really problematic then talk to the PI and suggest that with the individual's lack of experience he could benefit from working with a more senior group member/post doc. 

I'm not sure if I should feel insulted or not because I just found out someone from my cohort class got accepted to my program with UG 2.8 GPA, M 3.0 GPA, 1100 GRE (on the old scale), no publications/internships/fellowships/industrial experiences and failed all the ACS diagnostic exams.   If the admission process was truly merit-based, then an applicant with that kind of porfolio should never gotten accepted in the first place  . 

...Why is this a problem? What does it have to do with you?