A player has to be in an offside position, and commit an "offence".
Offside position
Sterling was inches offside, but you need video evidence to be convinced. It's so close I don't think in real time a linesman can give it after all a player is not in an offside position if level, and what is meant by level? Technically no player can ever be level. I am sure you could make an argument to say that a player is level if it is not possible for an observer standing 30 m away on the touchline to determine a difference. A players hands and arms do not come into it. It's the position of the torso.
Offside offence
The relevant part of the rule.....
- clearly attempting to play a ball which is close to him when this action impacts on an opponent or
- making an obvious action which clearly impacts on the ability of an opponent to play the ball
I think Sterling attempts to play the ball even though he claims he did not, but did it impact on an opponent? I would say yes to this aspect, but it's clearly open to interpretation.