I wanted to try my hand at hand planes (no pun intended), so went
to the borg and got a el-cheapo plane (6.5 inch buck bros, made
in USA, ~$12).

Got home and tried it on a scrap piece of 2x2, and after some
sharpening and adjusting could get very thin shavings off the wood.

Heres the problem - while most of the surface was satisfactorily
smooth, there were portions with tear-outs, that just got worse
on more planing. Is this related to the wood, sharpness of the
blade, depth of the blade, or technique?

DGS-ed, but couldnt find anything that might point to what I can
do to get better results...

Thanks,
Irax.