Generally people ask either because they're using the information as a basis to judge you, like in a job interview, or they're just making general conversation, and looking for a way to get to know you better.
In either case avoiding the question is problematic.
In a job interview it's downright foolish. Omitting this information or avoiding the question can only hurt your chances.
In social situations, you have a little more wiggle room depending on how the question is phrased. For instance if they simply ask where you went to school:
Oh, I went to school in sunny Florida. Nice and warm down there, but the mosquitos will carry you away.
This isn't exactly an abrupt change in subject, but it accomplishes the same goal socially. Chances are they'll be thinking about Florida, the weather, or mosquitos now.
More direct question wording will be more problematic. If they specifically ask "what school did you graduate from?" You may have fewer options for diversion. Here cheap jokes can offer some help:
I graduated from the school of hard knocks.
I've been kicked out of some of the finest institutions in the North East.
I feel your pain here. The list of highschools I attended is... well... a little problematic professionally and socially. One of them was so exclusive that you had to be personally recommended by a sitting judge.
Warning and disclaimer...
The sort of people who are going to judge you socially based on your alma mater are likely going to just find some other criteria to judge you on. Often any answer that isn't the school they went to personally, or a better school, will be a mark against you. Such people should generally be avoided, because they're generally awful and their cloud of smug threatens to consume us all.
Find a better bunch of people to socialize with.