Some introspection from someone who did take it personally at first:
We applied to YC last winter and got an interview, but ultimately we weren't accepted.
As a founder you're obviously incredibly enthusiastic about your idea and think it's brilliant, and YC is usually an early stop in a company's life. So, to hear a 'no' from a well-respected source before you even really get started is definitely an ego blow.
What mostly sucks about getting rejected is that YC says repeatedly that they accept teams, not products. So when we were rejected, I immediately took it as a personal affront: Clearly they didn't like me, my co-founder, or our dynamic, all of which inspired that (admittedly immature) defense mechanism of "We're great people, so you're dumb and wrong!"
However.
Once we had gotten over it and gone through the ringer of raising funding, you start taking it significantly less personally. Some VCs don't believe in entire sectors of businesses, so it's an automatic 'no' if you're in one of them. People can and will say 'no' because they're having a bad day, or you remind them of someone they don't like, or they had a bad experience with a similar company. Not that there aren't nuggets of wisdom to be gained from the 'no's, because obviously there are, but not every failure is a lesson necessarily.
All that to say, I think it's ok to take it a little personally. Maybe you should, even. But then you have to get back on the horse and get back to it.