Gee, I've rarely read so much misguided advice from people who have very little idea of what they're talking about.
1. Clarity - acrylic sheet (Perspex etc...) is many times clearer than glass, by a factor of ten to hundreds or more - it is used to pipe light hundreds of kilometres in fibreoptics etc.
2. Acrylic sheet scratches easily, the first time you wipe it over, you begin the process of degradation
3. Acrylic sheet is highly electrostatic - clean and polish it in a dry atmosphere and it will attract more dust IMMEDIATELY, and this is very hard to remove because the more you wipe it the worse it gets
3. Acrylic sheet absorbs water and expands on the side where the greatest humidity is, so it bows according to ambient conditions
4. Acrylic sheet is highly flexible, and as others have said, animals will escape if they put a bit of pressure on the overlap (one respondent had an animal escape THREE times???)
5. If you read the OPs first post, you'll see that the size of the sheets required is very large, the flex factor will be very great, making acrylic totally unsuitable, unless each sheet is fully framed
6. The only appropriate material for unframed doors here would be either laminated glass (preferred) or toughened glass (will have to be processed specially for this size), but you would need ball-bearing runners to support the weight.
Overall, as Snowman said, acrylic is a crap material for animal enclosures - I spent years with the stuff as showcase material, working in museums. Compared to glass it makes for a massive amount of extra work, is unstable for the reasons I've outlined, and generally has a relatively short service life. I wouldn't touch the stuff for this application.
I don't know where the comment about it being cheaper than glass comes from - the respondent obviously hasn't shopped around for glass...
Jamie