Is this unfair?

I started a new job in June on a temporary 3-month contract. I work with another girl in my year pretty closely, we’re call handlers. She started a bit earlier than me. Recently, the company have been messing up our holiday. I had a day off about a week after I started as I was on holiday. I didn’t have access to our holiday booking portal so didn’t note down the day I’d had off. Once I got access to the portal, I figured they would add that day in for me. They didn’t tell us that our bank holiday hours in August are removed from our holiday, so we have 7.5 hours less than we thought we did. However, I went to book off a whole week in August as I have university re-sits to do, not because I failed, but because I didn’t do as well as I wanted to. Anyway, because I had the day off in June that I didn’t record, they won’t let me have a whole week off. I also have 2 days off at the end of August for a holiday and they were trying to get me to drop one of those days so I can have a full week off. I can’t do that because my boyfriend has already booked those days and he rarely gets a holiday. Anyway, I contacted my manager and asked if I could take the day as unpaid so I have a full week off to work on my assignments. But he won’t let me. He said unpaid annual leave is for exceptional circumstances, is he in being unfair or am I being naive? Let me know your thoughts.

Quite a few places won't let you go over your holiday allowance. Places might let you have time off unpaid, but that's their discretion.
If they have messed you about with your holidays like you say then that's their fault.
In my opinion, uni resits would count as being important. I'd speak to them again, tell them in no uncertain terms that you have to have the time off for uni resits. Tell them that you can have it unpaid if possible. And tell them that the holiday with your boyfriend was booked before you started there. And tell them that whatever happens, you will be off (wether they put it as holiday/unpaid/whatever).

Yeah, I understand that. They’re letting the other girl I work with have one of her days of holiday as unpaid because they didn’t take the bank holiday out of her holiday entitlement, so she overbooked holiday. I really don’t think they will let me do that, my manager seemed very snotty in his email responses. I haven’t ever met him in person because he mostly works from home. I had 3 unpaid sick days during my probation and I think they’re still bitter about them. Even though, they were genuine and I offered to provide them with a doctor’s note if they wanted it. I don’t really know what to do now, but I feel very slighted about this.

I'd still email back saying that you HAVE to be off for your uni resits. And that you will be off (wether it be down as holiday or unpaid). And if need be, remind him that it was them that messed your holidays up to start with.
If they messed your holidays up then that's their fault.

I'd still email back saying that you HAVE to be off for your uni resits. And that you will be off (wether it be down as holiday or unpaid). And if need be, remind him that it was them that messed your holidays up to start with.
If they messed your holidays up then that's their fault.