Time doesn't exist?

I'm not sure that I completely followed your argument, but anything could be argued to not exist, including existence itself. As they say, perception is reality. My logic would also follow that if perception is reality, and perception is subjective, then reality is subjective. We all choose the worlds we live in.

According to current theories, what we call time is just another dimension in space and which is now defined as space time. All things exist in space time which consists of the three that we can see, and one that we can't see and which we call time. This is the simple version. In fact it's theorised that there are many more dimensions than those four. If you could see an object in four dimensional space time you would see that what we normally see is just a three dimensional cross section through a four dimensional object. Rather like if you took a cube and sliced it in half you would then have a two dimensional cross section (a square) of a three dimensional object. In short, what we call the present is just the point on the four dimensional object which is our body, at which our mind exists. It might also be said that mind itself is existing in four dimensions so that everything that we have been and everything that we will be already exists in what we call the past or what we call the future. In this scenario, free will is either an illusion or, taking the multiverse theory, there are endless future possible realities which may or may not exist alongside our "own" reality. There are other theoretical possibilities as well. The conclusion is that you are correct in saying that time does not exist, at least not in the commonly understood sense, because what we call time is simply another spatial dimension which is not fundamentally different from the three that we are familiar with.