How to train the pet?
Training your pets will also increase its closeness with you. Basically, you can train it in three ways:
1. Feeding it
As above. ^^
2. Giving it commands to follow up.
Check out the command guide below for each pet's respective commands. If your pets follow your commands, the closeness will increase. NOTE that different command levels will give different different amount of closeness. E.g. lvl 0-10 commands give +1 closeness, lvl 10-20 commands give +2 and lvl 20-30 commands give +3. Spam the commands for your pet's corresponding level to get more closeness. Giving your pet a name and using its name in the command will also increase the chance of increasing the closeness. Also note that there is a certain time frame for certain pets to successfully follow a command, for instance, every 10-20 seconds. So instead of spamming the commands every second (and keep getting negative responses from your pet), try to space out your commands.
3. Doing the Pet's jumping quest at Henesys and Ludibrium.
Henesys's Pet Walking Park Ludibrium's Pet Walkway
Talk to the NPC in the park before embarking on the jumping quest. Each time you successfully complete the quest and talk to the other NPC at the end of it, your pet's closeness will increase! The jumping quest requires a lot of patience and time, so be patient and have fun during the process!