To be honest, some phrasal verbs don't have a "logical" explanation. Native English speakers hear phrasal verbs from an early age and truthfully, a lot of them don't make logical sense. Sorry, but it's the truth! I recommend finding tricks to memorize them for that reason.
Try imagining the following to help you remember:
For "give up", imagine someone throwing their hands up in the air as a sign of surrender or defeat. Have you ever done this when you felt defeated by something? I know I have!
For "give in", you can imagine someone that has built up a strong fortress to keep out something they don't want. Only the fortress wasn't strong enough and their fortress caves in or "gives in".
Eg. I gave in to that extra piece of chocolate, or I allowed that extra piece of chocolate into my mouth.
I hope these scenarios help you a little. I commend your efforts to learn phrasal verbs. A good understanding of phrasal verbs will help you to sound more fluent in English. Don't give up or give in when it comes to learning them!
If you're interested in taking English lessons, we can discuss a variety of phrasal verbs and tricks you can use to remember them! I am a professional English teacher and English is my native language. I do my best to make learning interesting and fun, and I am currently accepting new students.