I am astounded how many people in this thread can't see that being late for work/school is unacceptable behaviour.
I run my own construction business, and many times my overall crew cost will be over $1,000 per hour. If my lead operator is late a few minutes, the entire crew stands there waiting for the work to begin, costing the company significant money. This is not acceptable behaviour and I have fired more than one otherwise good employee because they couldn't get their act together and show up on time.
In my office, I expect everyone to arrive on time unless they have let me know ahead of time they have another commitment. If one person starts showing up late, and consistently gets away with it, other employees will start to stretch the rules as well. If someone needs to arrive late or leave early, I am more than willing to give them the time, but don't try to take it for granted without asking first.
Secondly, sure school is not quite the same, but a good professor will be trying to instill the correct habits in his students from day one. If he says be on time, that is the rule, no exceptions. If he starts making an exception for the OP for 2 minutes 9 times in a semester, next semester someone will be asking for 5 minutes 10 times.
Regardless of it being only 2 minutes late, it can be extremely disruptive to everyone else attending the class or meeting. Everything stops while all eyes go to the door to see who is late and watch them find a chair and settle in. It is human nature.
In university, I had a prof who stood by the door until class time, and then closed it. He made it clear that if you weren't in the room when the door closed, you better not open it unless you were there to warn them of a fire. If you were 5 seconds late, you missed the class. Sure, I ranted about it to my friends, but I learned my lesson and I was in my seat before the door closed 99.9% of the time.
 edit: for typos.