Maybe need to qualify what leaning towards sciences means. Often degrees that require sciences also require maths.
I'd also agree that doing it early may not be best if he's going to require it at a level, will he be straight into studying it next year?
It's simply a lot of kids who get a star in maths GCSE struggled with a level, not as in fail, but they struggle to get the same A star at a level, depends on the kid. My daughter got a star in maths, and considered it, in her words "an easy exam" and most of the kids feel the same. She didn't do maths A a level, but the ones who did and also got a star, felt the leap between the two was huge.
There's always a big leap between GCSE and a level, but for some reason, maths is the one most of my daughters friends felt had the biggest leap.
There's nothing wrong with being pushy, as long as it's not too early or damaging to the kid and is simply helping them achieve their potential. Some kids are lazy little sods and do need a bit of a push.
I didn't push my daughter, because yes the sdhool did. im not sure if say uni does, but they like to pile on the work..😂