My boyfriend (21M) doesn't want to call me (21F) "baby" because he used to use that word for his ex

I have been dating him for the past 5 months and till the first 3 months, everything was good between us like it is in the initial phases of a relationship. We both are in our final year and he has some academic backlogs because of which he has been stressed abd since then there have been some problems in our relationship. Since the end of March till today's date, we have only met thrice, we hardly even get on call because he's busy with classes and projects and all our conversations are serious these days

since end of March he had been mentioning his ex girlfriend a lot. He used to constantly tell me how much effort He had put into their relationship ( which was 5 years ago) but they had to end it because her parents were super strict and how he had a very hard time moving on from that. He said he wasn't ready for relationship until he met me because he has been scared of getting into one since that breakup which I totally understand. Our relationship was also on the verge of breaking up because he said that he wants to focus on his career and relationship is not a priority for him. What j feel is, constantly reminding me about how much effort he had put into their relationship.. doesn't look nice. ( at least to me)

He used to call me all sorts of cute words since the start of our relationship and infact he was the one who started calling me "babe" "baby". I wished him "Goodnight babe" yesterday night and he responded with with " i love you good night" and hearts. I just joking texted him "at least call me babe/baby mannnn" He responded by saying "that doesn't look good, calling you by your nickname is better" so i asked him "why does it not look good" he said " i dont have a habit of calling someone baby/babe" . Later after a bit of conversation he said " im sorry i cant call you that because i used to use that word a lot for my ex"

Tbh I didn't have any problem with not being called "baby" I only had a problem with the reason he gave me. Made me feel like he is stuck in the past. Isnt baby just a word? When I brought this concern up his replies were" yeah I'm still stuck in the past, happy?" , "think whatever you want to think I don't care" , " I'm telling you last time please don't irritate me so much" , " I was already hyper because of my exams and now I'm more hyper because of these texts ".. and I just dont know anymore. We don't meet or get on calls. We have met only thrice since march so reassuring me that he still loves me, saying cute things on texts or being romantic over text is the least that can be done since we are apart, i feel.

TL;DR: boyfriend has been mentioning his ex a lot and how much effort he had put for her, how his whole world used to revolve around her. He dosent want to use "baby" because he thinks that it is weird to call me that because he used to use that when he was in a relationship with his ex (5 years ago) Is that a valid reason to give?