Obelisk the Tormentor VS Earthbound Immortal

I was in a duel and I had an earthbound immortal in play.

My opponent played an obelisk the tormentor and claimed that he was able to attack and kill my earthbound immortal on the claim that the summoning of obelisk negates all other card effects. I explained to him that it only negates effects that target obelisk specifically when he is summoned and when he is in play. He then claimed that not being able to attack my immortal was a target upon his god card and said he should be able to attack me. I don't think he should be able to because I don't see how an effect of not being able to be targeted means that I'm targeting any of his monsters specifically.

Continous eff cann't be negated

As spirit reaper vs Shadow Imp. Mirror

Of course you are right. It's like saying that Gravity Bind targets.

Just a quick thing:
You can't activate ANY card at the time of Obelisk's summon.

That out of the way you are correct in that EBIs do not target with their "Cannot be attacked" effect, due to it being a continuous effect.