というものでもない

というものでもない means "it isn't necessarily so": you take an assumption people make and say it does not always hold. It follows a plain-form sentence, very often a condition with ば and the result people expect from it. A noun or な-adjective can take だ before という or go without it.

The assumption is not called false, only too simple, and the next sentence often says what else counts.

でもない or ではない

でも makes the denial softer than というものではない: "not necessarily either", leaving room for the assumption to be partly right. ではない is the firmer correction.

というものでもない or ものではない

Without という, ものではない is a different pattern: "you shouldn't", a statement of what is proper. というものでもない is about whether a claim is true.

In conversation it shortens to ってものでもない.