The thing is, it's best for Sterling's development if he stays
If he takes 90-100K now, he'll probably be on loads more than 150K in a couple of years anyway if he continues to develop at the rate which he is
I mean, he's not going to be struggling on 90K a week is he?
Take that now, improve as a player and then take a massive contract in 2-3 years time when you're actually ready to justify one. Thusly, you'll then be "juiced in" as a big contract player forevermore
There's a strong chance that he'd go to City/Chelsea/Royal Madrid in the summer and flop there because he isn't ready. Sure, he'd get maybe a year or two on 150K, but he'd never make anything close to that again as he'd be just another promising young player who flopped at a "bigger" club (i.e. Rodwell)
If he stays at Liverpool, he can continue to be a big fish in a comparatively smaller pond and get a big move in a couple of years
The agent should realise this and be making it clear to him. Both agent and player are lacking foresight here
I've said it before but I honestly feel players like him have a shorter career at the top level. There aren't many small, fast players going strong towards their 30's. Most of them drop away in their mid 20's due to physical limitations.
He seems fairly clued in, he joined them as a stepping stone and now wants to make the next step up while he can. They proclaim he's World Class and all this, yet he's not even their highest earner. They're unlikely to win major honours either. It's not guaranteed he'll improve as a player, especially if he's essentially (as they put it) their best player.
Stay - less money, less chance of winning trophies, potentially a big fish in a small pond.
Leave - more money, more chance of winning trophies, potentially more opportunities to learn by training with better players.
As a footballer you have to have confidence in your own ability that you can succeed. Surely it's a no brainer, why would he stay?