Today I met a black cat. I really wanted to bring him up (ha ha). I assume it was a stray, but I haven't met it before. I thought it very special to meet a black cat, so it has an odd appeal to me.
今天看到一只黑色的猫,我好想它他领回家哈哈,我猜它是一个流浪猫,不过我之前没有遇到它。对于黑色的猫我觉得很特殊,所以它对我有种重莫名其妙的吸引力
I think your sentences contain no actual grammatical errors! "Bring him up" is correct, but I am not sure it means what you think it means. It means "raise". It means you will feed him and take care of him as he grows. Parents "bring up" their children.
You use the past tense more than you need to. That is not a mistake, but I just want you to know that you have the option to use the present tense more. The present tense can be used for past events if there is no real need to establish a time frame. For example, you can say "I GUESS it was a stray cat", rather than "guessed", because the precise time when you guessed has no importance. You can even say "I guess it IS a stray cat". It is a timeless thought, so present tense is actually better. You can say "it HAS an odd appeal to me" because the moment when it appealed is not something that matters. If you consider it important to specify when exactly it appealed to you, you certainly can use past tense. For instance, it may have appealed to you yesterday but no longer does.