There are so many reason to breed your tiniquines! That is the main focus of owning tiniquines.
Acquiring more tiniquines.
The first and probably the most common answer is to get more tiniquines. Breeding can help you get acquire more tiniquines faster than waiting for a sale or raffle, or someone else to sell a tiniquine. If you want to get more tiniquines quickly it is best to buy mares first and breed them.
Some other reasons could be, but are not limited to:
Breeding to get a certain color.
If you are trying to achieve a certain color then breeding is your best bet, rather than waiting ages for the right tiniquine with your markings to come along in a sale, if it ever does.
Breeding to get certain markings.
If you are trying to achieve a certain pattern or certain markings, just as well as color, breeding is better then to just sit around and wait to see if it's ever offered at a sale.
Breeding to get certain genetics.
If you have a tiniquine with a certain phenotype and are looking to add another to it's genotype then breeding is a good way to cross genes and get the ones you are looking for.
Breeding winners to produce would be winners.
If you have a champion stallion or mare and breed it there's a very good chance you could get champion foals as a result of breeding it.
Breeding is also fun, you never know what you are going to get.