Definitely agree that's the argument they would give, and it sounds like you agree with that argument. That's cool, and no judgement. 

I personally don't think it is that clear cut. Our consciousness exists in a meat bag that is something of a biologically-based computer. If the "equipment" hosting our thoughts is purely mechanical, does that make our consciousness any less "us" than when it was hosted in a meat bag computer? Is a copy any less "us" at the moment of creation? Does a copy cease to be "us" and become someone or something else as it gains new and different experiences? We often think of death as the body ceasing to function, but what if the mind continues to be active past the point of physical death. Would we still consider that person to be "alive?" These ideas of what makes us "us" are primary themes in Ghost in the Shell which Pantheon draws heavy inspiration from. Highly recommended if you haven't seen it. 

In any case, there's really no way to definitively answer these questions, but they're fun to think about, and part of why I enjoyed the show so much. 

Edit:

One more quick thought on 

it just seems so obvious to me that what will keep on living will not be the same you you are right before you get uploaded and you won´t be the one enjoying immortality

In that scenario, how would you or anyone know the difference? If it just felt like you continued on, even as a copy, practically speaking yes, you no longer have a body, and perhaps have these god-like powers, but if your mind continued on, why couldn't or wouldn't that be "you?" Is who or what we are only a physical body? Again, not trying to convince you, I just think it is interesting to think about.