There are always threads on MN about this situation.
It could be anything.
If you're 10/20 years younger than them, they might assume you already have your own friends outside of school and aren't interested in them.
They might see that you're younger and assume you'll have nothing in common.
I had no interest in making my own friends at the school gate but did want to facilitate my children's friendships.
Find out who your daughter plays with at school. Approach the mum on the playground and smile.. Invite the child round for tea or to the park after school. Ask them if they'd also like to come for a coffee and a chat while the childen are playing.
Despite what you read on here, I think most parents have their own friends outside school and busy lives so aren't really looking to make friendships at the school gates. Some parents live near each other or met at baby groups so have already established friendships before their child starts school.
I'm quite alternative looking and so no one was rushing to be my best mate in the school playground in my very stylish middle class neighbourhood! 😁 but I still arranged coffee meets, invited their children round to play and made close enough acquaintances for my children to be included.
If you just want to find a friend for yourself, find the mum who is also standing on her own or the one who alsp appears to be a bit of a misfit 😉 but there's no guarantee your childen will also be friends.
You need to he proactive in this if its what you want.