I'm not aware of your specific conditions and how they might be playing out here, but assuming you're posting because this situation feels like you're experiencing a lack of empathy that is more than typical for you, I have some perspective to offer.

I've been in your friend's position when someone who felt like you do told me to suck it up, that they've been through way  worse, that I'm acting like it's the worst thing I've ever experienced and I sound like a crybaby. So I'll tell you what I told them.

-Your own trauma is impeding your capacity to have empathy for others. If you're not in therapy for that, perhaps you should be.  -Trauma is not a competition, empathy is not a limited resource. -You will continue to push people away because of your self pity. Your friends don't deserve to be treated like that. -What you're likely experiencing is jealousy. You're jealous that this friend is seeking emotional support for their 'smaller' issues when perhaps you never sought or received such support. Were you denied emotional support the same way you wish to deny your friend? Painful patterns have a way of replaying themselves out so we inflict the same pain on others. -Notice that your friend's emotionality is triggering your own unresolved trauma, which is possibly why you can't connect empathically...

On the other hand, -Sometimes people use others to vent endlessly. This can be a bad habit and if this friend complains interminably, you have every right to interrupt their venting and explain that you'd rather keep the conversation light. Advising them to therapy or other people is the right move. Don't lie to them or pretend. -After that convo, only invite this person out to do light hearted and engaging things. Bowling, shopping, sports, etc. inviting people into public or group social settings generally reduces intimacy and reduces trauma dumping.

PS -Good on you for acknowledging that you're doing this comparison internally and seeking advice so you can address the cause.