“So who were you? I saw your height and your hair, but I couldn’t see your face clearly enough.Still, you gave yourself up, Tyler. The next day at school I asked so many people the exact same question, Where were you last night?”
Excerpt FromThirteen Reasons WhyJay AsherThis material may be protected by copyright.

That doesn't make any sense.

To give oneself up is to surrender to the enemy or to the authorities, to turn oneself in. There are no enemies or authorities in evidence in the brief passage you cite.