The main argument I could see for a big crunch (and I mean big crunch in the conventional way it's talked about) as opposed to heat death is that we may well still be in the middle of the big bang.
For example the big bang is talked about like an event that happened at the beginning of time, a big explosion that spread everything out. We have observed that our universe is expanding, is this due to some other force than that force of spreading, that explosion that began at the big bang?
People seem to think that the observation that the universe is currently expanding runs contrary to the idea of a universe that expands and then eventually collapses.
May well be that the universe will simply expand indefinitely until heat death, but there doesn't seem to be any more evidence for that route than a big crunch.
Now
@Iximi If you define big crunch as being the point when the positive universe achieves maximum entropy (i.e. everything is spread evenly and any change in position or energy of anything would add order to the system) how is that different from a heat death type scenario and what is the point of the negative universe? Your negative universe seems to me to be just looking at the positive universe backwards. What observations are the existence of the negative universe supposed to explain, and what observations are this theory as a whole supposed to explain?
Why phrase it in terms of positive and negative universes and entropy/time?
It is hard to disprove a theory such as this, but sometimes it is also hard to distinguish it from existing theories, simply defined using a new set of words.
I would recommend laying out some formulas and predictions if you wish to take this theory further. What advantages does your theory offer over others, and does it offer any correct predictions?
I have a lot of fun coming up with pet theories too, I also recommend going over to the physics forum and looking at other peoples' theories. The people there are generally pretty open minded to new ideas too, and can help you further develop your theories.