I don't think I understand
Are you mad because he got his bike back and didn't give the kid a pasting or because he didn't arrest him?
If he's off duty and he's just after his bike like any other normal citizen then job done what's your problem.
If he gave him a pasting, then that's his job, career and chances are most of his mates gone.
He arrests him for being in possession of a stolen bike, first question to any civilian can you prove it’s your bike? “Did you just go after a kid on a bike the same as yours and conveniently get it back?”- it’s a whole can of worms.
And to make matters worse there’s no proof the kid on the bike is the thief not to mention the p155 all sentence he’d get out of it (thanks CPS)
And as already pointed out if it all happened in his back yard so to speak then there is the family element too to think of. If the kid on the bike is the thief then he knows where the cop lives so can send his mates round to put a brick through the window or steal the bike again.
All in all you sound a little too angry about what is ultimately a happy ending
Bloke gets bike nicked. Bloke gets bike back.