There are a few verbs in English that tend not to be used in their continuous (~ing) form. Belong is one of them. Simply, something belongs or it does not.
He belongs to the rugby team. CORRECT
He is belonging to the rugby team. INCORRECT
There are two times when you can use ‘belonging’, one as a noun, one as a gerund (~ing verb used to describe an action as a noun)/
Whose belonging is this?
Even then, it is normally used as a plural (‘belongings’), or would be rephrased as:
Who does this belong to? (STRICTLY INCORRECT BUT MOST COMMONLY USED) OR
To whom does this belong? (CORRECT BUT SELDOM USED)
I like belonging to the dance club at college.