のはXの方だ【のは～のほうだ】

のはXの方だ picks out which of two sides fits a description: "X is the one who ~", "it's X that ~". The description comes first, turned into a noun with の and set up with は; the answer comes last with の方だ. A verb or い-adjective takes のは in the plain form; a noun or な-adjective takes なのは.

The 方 means "side", and it is what makes the sentence a contrast: X and not the other one. It turns up most where blame or credit is being sorted out: taking the blame yourself, or pointing it back at the other side.

With and without 方

Without 方, のはXだ simply names who or what it was. With 方, there is another candidate in the background, often the one just mentioned.

Comparing qualities

With an adjective, the pattern says which of two things has more of the quality, as in a comparison with より.