grammar - What does why would I do it mean in this context?

I've often heard people saying this. And even I say it when someone accuses me of doing something that I didn't do.

I'd say:

Why would I do that?

But what's the grammar behind it?

Is it future from the past tense or something or what? It's obviously not a conditional construction 😒

Context from SE01 EP02 Austin & Ally

Austin: what does the jacket have to do with the music video?

Trish: It's a line in Ally's song, "my jacket's in the lost and found."

Ally: "my jacket"? It says "I like it." The line is "I like it when you hang around."

Dez: "hang around"? I thought it said "kangaroo." ♪ I like it when you kangaroo. ♪.

Ally: Why would I write "I like it when you kangaroo"?