I was a FT teacher with a baby (and then a toddler and a baby) with no family around. I love my kids and I love being with them, but I'd take the 50% during school holidays without blinking.
A) have you ever, as a teacher, NOT worked during school holidays? It's either a couple of days on reports, or catching up with marking, or in school at the chalkface doing revision sessions/exam results, or setting for next year after doing exam results analysis, or cleaning my classroom. Having the 50% option would allow you to do this.
B) I know exactly what it's like - term time you're getting home after a day at work, tea, play, kids to bed, then starting to work again at 8pm-midnight. Living for the school holidays when you can go to dentist/hairdresser/clothes shopping/visit a friend/sleep. If you have a couple of days in the holidays to do that, you will be able to spend the other days actually doing nice stuff with your child. Days out etc.
C) I love my kids and I enjoy spending time with them. I'm also a person with my own interests and needs. There is nothing wrong with building some opportunity for this into your life.
D) I don't think people who have family help always understand how hard it is without. I couldn't pop to the shops (or pop anywhere - it was an epic trip out or do without), or have someone watch baby for 30mins while i went to doctors, or have someone take baby for a walk while I lay on the bed crying, or on the sofa watching NOT cbbc.
In conclusion, I'm sure I don't actually have to tell you that you are allowed to have some time to yourself to do whatever you want. It doesn't mean you don't love your child. Also, and I have quite a bit of professional experience in this, there are lots of benefits to spending time in nursery with other adults and children. Your child may even enjoy it 😉.