Why aren't human babies considered larvae?
For animals with a clear larval stage, the presence of such a stage indicates that there is a metamorphosis, a change in body morphology at some point in development.

Metamorphosis does not necessarily refer to an 'instant' transformation or one that requires a pupation step or something similar; gradual change can still be metamorphosis, as long as there is a clear 'before' and 'after.' 

Human infants, on the other hand, don't go through much of a metamorphosis: sure, they grow quite a bit, but their general body plan does not change. Contrast this with insects, or your tadpole example, and it is clear there are major body plan changes from larvae to adult stages.

The Wikipedia page on larvae describes the characteristics of larvae fairly clearly. Like most traits in biology that vary across taxa, you are likely to find some intermediate creatures where the presence of a larval stage is somewhat controversial or depends on opinion. There could be a difference of opinion on how much of a change is sufficient to describe a juvenile form as a larvae. Humans don't have a postnatal stage that approaches that potential boundary.

The part in your question about people who are "anti-baby" sounds a bit judgmental, but I think what you are describing is just a phrasing meant to be somewhat humorous and to evoke images of "gross" larvae; I wouldn't take that for any biological meaning and I wouldn't focus your time on proving it "wrong" - the actual difference of opinion you have is something entirely different.