Saying that the Democrats are to the left of the Republicans doesn't make the Democrats "left", it only makes them "less right".
I know, but that isn't what I said. Neither the stated philosophies of the Democrats nor the Republicans are the center point. You can be a little to the right of the Democrats and still be left wing. (That philosophy is called "Classical Liberalism.") Similarly, you could be a little to the left of the stated position of the Republicans and still be right wing. "Failure to advocate for out and out socialism" isn't the dividing line for right wing versus left wing. If you talk like it is, you're being deliberately unclear.
Also of note, the guy who started this whole argument off wants to vote** for Bernie Sanders, who is a Democrat in the sense that he's running for the Democratic nomination, but who is not a Democrat in the sense that he's been registered with the Socialist part for most* of his career.
*I assume that you need to register as a Democrat to run in the Democratic primary, and thus Sanders is registered as a Democrat now. If he doesn't, he's probably still registered with the Socialists. I haven't actually checked, mostly because "Bernie Sanders is a Socialist" is a well known fact.
**The guy says he wants to vote for Sanders twice. So he may well be a Democrat, just one of the ones on the left wing of that party.