Rare pigs becoming a ★1 Hybrid (raising unsuccessful)
Answer
A pig's breed is determined when you buy your piglet, but there are certain criteria which must be fulfilled. If they are not, your piglet will turn into a ★1 Hybrid.
The number of criteria and their difficulty is different depending on the pig, but the main ones are as follows:
1. If pigs have feed preferences, they'll need to be fed what they like. (If there are several, feed all of those kinds.)
2. Some pigs will need to be grazed.
3. Pigs will need to be fed over a certain number of times (varying by type).
4. Pigs will need to be over a certain weight (varying by type).
If your rare pig ended up becoming a Hybrid, it's because one or more of the above 4 criteria were not met. The higher the number of ★'s, the harder it will generally be to raise your pig.
Further, Legendary pigs obtained from hunting may have additional criteria. They're not explicitly mentioned, so you'll need to work out the details from the raising tips.