Why do teenagers just want to spend everything they’ve got?
They don't, all.
Some do some don't. I've had 3 teens. One earned his money and liked to spend it. One earned and saved almost everything. One is somewhere between the two.
So he knows he has his own savings account and thinks it doesn’t matter if we don’t give him money as he’s got his own right there and it’s his right to use it.
I'm a bit confused - how has he got money if you aren't giving it him ? Do you mean something say that Grandparents gave him when he was little ?
Before they were 18, mine couldn't access money they'd been given for saving. It was in Premium bonds of Building Society account in my name as a trustee for them.
Do these sound reasonable or would you give more/less?
I never 'paid' mine for contributing around the house. They are expected to contribute because they live here. Don't get me wrong, they all went through stages when their rooms were total pits, but that was a separate battle from teaching them about budgeting and saving.
However, if you have set up his money as pay for jobs, and he isn't doing the jobs, then why are you giving him the money ? 
Why is it so hard to teach teens about money habits?
I don't think it is.
It starts from when they first have pocket money, (We started ours when they were 7), the idea that 'you have £1. When it is gone it is gone. You can spend it each week, or you can save it to buy {insert whatever they like / want at the time}, or a combination of the two.
Over the years, you have conversations about things like how much less you pay if you save for something, rather than take out credit. General conversations about money management.
If you are giving him £20 every weekend, he has no need to learn to budget, or to value money.