It's thought that life began here in the absence of oxygen, and only over time did oxygen begin to play a part in cellular life. As another poster points out, there are still some cellular organisms here that do without oxygen, indeed they would find it toxic.
> I always wonder why alien life or any other life cannot happen without it.
But that's not true, not even here. Oxygen is regarded as a sign of life, but its absence doesn't suggest the absence of life, only the kind of life that requires it.
If by oxygen you mean molecular oxygen, O2 -- rather than atomic oxygen as part of some other compound -- we know life can happen without it, since there is life on earth that lives without it. And, IIRC, we have strong reason to believe that life that could live without O2 predates life that needs O2, and, in fact, it is life that made free O2 available, not free O2 that made life possible.
Yes, early life on Earth was all anaerobic. That started around 4.1 Gya (billion years ago)[1]. The Great Oxygenation Event[2] happened around 2.3 Gya - that wasn't the first appearance of photosynthesis, but it was the point at which it changed the atmosphere enough to wipe out most of the other life on Earth at the time. Obligate aerobes - organisms that need oxygen to survive - were later still.
[1] https://en.wikipedia.org/wiki/Timeline_of_the_evolutionary_h...
There are good reasons to believe that ours is quite likely and good reason to be skeptical of alternatives, in the proper scientific sense, but certainly not disproved or something.
Undoubtedly. The problem is that very few people, even among the well-educated and technically proficient, actually form their views about the state of science by talking to scientists.