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Anyways, when I tried pushing, his goons and zealots destroyed my force (why did my force die?)
Because his forces attacked your forces, and caused enough damage to them to deplete your unit's HP to zero, thus causing them to die. And conversely, he was able to do this to your units faster than you were able to do it to his units.
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So I tried to play defensive and set up my third, but he easily destroyed it (again, why, and how should I have defended it?).
Well, your 3rd was destroyed for the same reason as your earlier push died. He caused enough damage to your units and such, so that they exploded and died. You could have defended it if you had the units in place to kill his units.