One of the rules about the French subjunctive is it applies to phrases that express possibility, so it's unsurprising that the expression il est possible, which means "it is possible" in French, requires the subjunctive.
Il est possible qu'il le fasse.
It's possible that he'll do it.
Il est possible que vous ne l'aimiez pas.
You may not like it.
Il est possible qu'ils aient raison.
They may be right.