AITA for keeping my ex boyfriends jacket

About three months ago, I (f19) met a guy (m19) on an app. At first, it was bumpy. We didn’t really talk that much, then all of a sudden, we started talking. We clicked on every level. We talked every day, called every day, and played online games when he had time. After about a month, I went out to see him, spending about $400. He lives in the Bay Area, and I live in Northern California, so it was about a four-hour drive or a six-hour train ride. We really hit it off in person, or so I thought. I met his parents and thought they liked me.
After a couple of days, he messaged me, telling me that his dad said I wasn’t good enough. He said he didn’t care what his dad thought, that he really liked me, and I was sad, but, you know. After that, my boyfriend told me that his parents had bought him speed dating tickets and wanted him to dump me, but he said he didn’t care and wasn’t going to do it.

We continued dating, and a couple of days ago, he finally came over to my apartment. He came up to Northern California and was supposed to stay for three days, but on the second day, I was on his phone, and he got a message from a dating app. I stupidly tapped on it and saw that he was texting girls on there, and it was recent. I didn’t know what to say, so I went outside and talked to my friend. Then, I texted him about what I saw, and he completely gaslit me.

When I finally went back into the house, I sat on my bed, put my headphones in, listened to music, and fell asleep. After about an hour, I woke up, and his stuff was gone. He was gone, and all he left was his trash, a 49ers blanket, and a 49ers jacket. I thought it was ironic that he left it. I was lost. I looked everywhere, walked around the block a couple of times, but couldn’t find him. I even went to the train station to look for him because his train was supposed to leave the next day. He blocked me on everything. Finally, about an hour after I got to the train station (because I was just sitting there, not knowing what to do), he called me and said, ‘I’m at a hotel. Don’t worry. I’m sorry this had to be this way. Bye.’ I cried and cried when I went home and cried some more. I found out he left his jacket and didn’t know what to do with it, so I just put it in my closet.

The next morning, I got a message asking me to send the jacket in the mail. I said no. You disappeared, didn’t say bye, and blocked me on everything, so you don’t get your jacket back. Then, he went on to tell me how it’s sentimental to him, how he was wearing it when a war started, and how it connects to his people. I know it’s the right thing to do, but I don’t know why I can’t give it back to him. It’s not out of malice or even because I miss him.
I mean, I do. All I wanted was him. I mean, I loved him.

Should I send it back or is he being ridiculous?
Please no hate I’m just so confused and I can’t tell if it’s my people pleaser side that’s saying give it back or my moral compass saying I have to give it back to him.