Two reasons:

Performance

A lot of people have done extensive studying, and have determined that ID selectors are slightly slower than class. However, the difference is so marginal, it's almost not worth mentioning. If you use ID's in your CSS you won't notice a difference. However...

Specificity

This is the main reason people(like myself) don't use ID's. If you would like more info about this: Mozilla Developer Network

But basically ID's get a higher priority than anything else. So overwriting can become a huge pain, this is especially annoying in larger sites.

Here's what I have to add to Alex's comment :

With great power comes great responsibility - What if this specificity can be taken positively? It depends on how organised is your CSS. I think using ID selectors can be very useful at many places.

Too much specificity in an ID selector. Read those articles to understand:

• Specifics on CSS Specificity
• CSS Specificity: Things You Should Know