So is the point in breeding to get animals with higher points each generation?

Is that the main goal here on HP?

That would be the main goal imo, yes. You want your foals/pups born with the highest points possible so most players breed close to retirement (18 & 20 for horses, 13 & 15 for dogs). 

But there are tons of other goals too! You could try to get a foal with a full pedigree, have a pair hit a certain point goal amount (most players aim for at least 1 million by retirement), dedicate lines to real life animals or something with meaning in your life and set goals for that line, and there is a ton to accomplish on the achievements list that you can find here -> https://horsephenomena.com/other_info.php

You can also get involved in clubs and enter your animals in monthly contests, and join / participate in breed embassy activites.

My personal goal is to -someday- have more accounts so I can easier fund/train a high pointed project. But that is wayyy off.

Thanks guys!

Kyuubi, That's why I've wanted to go with Rotties. I used to have one IRL and she was the best dog I've ever had.