I feel that one of the best ways to learn, progress, and gauge where your skills are at (besides competition) is to train with different people and visit other gyms. I've learned some great stuff from just talking and bouncing ideas around with different people.
I love it when visitors show up to the gym, and I get to roll with new people. Usually, their game, body type, or technique is different from what I am used to. My mind is forced to think in alternative ways, and I find it challenging and exciting.
Now, of course the question comes up, "Am I being loyal to my instructor by training with another teacher"? I guess that all depends on your instructor and his/her feelings on the matter. Common sense would tell you that if you are interested at all in training at another gym, to first run it by your instructor out of common decency and respect. There's no reason to burn bridges.
I remember one of my instructors (I have three) telling me once, "I don't care where you train. I just want you to get better. You can train anywhere you want and anybody can train with me. My knowledge is for everyone". Hearing those words really meant a lot to me and made my already deep rooted loyalty and respect for my instructor even stronger.
Here's an interesting story:
One of my instructors, Park Jun-young received his black belt from Roberto Tozi. Now, Tozi is a student of Roberto Godoi. At one time, Roberto Godoi owned and operated a BJJ gym with his good friend Jorge "Macaco" Patino. After five years, the two had a falling out over finances. Godoi started his own gym and "Macaco" started his Gold Team gym. Roberto Tozi and Marco Barbosa (my other instructor's instructor) decided to stay with Godoi. Still following?
At this point, the two absolutely despised each other. They competed twice against each other with Godoi winning one match and "Macaco" winning one match. In 2006, they were offered money to fight in an MMA match against each other and "Macaco" TKO'd Godoi in the second round. Later, Tozi went on to compete against "Macaco" defeating him twice.
My instructor told me this story in passing once or twice. Well then imagine my surprise when I saw pictures of him training at "Macaco's" gym. I immediately became confused. I asked my instructor, "You trained with "Macaco?! Tozi and Godoi didn't get mad at you?"
He just laughed and shook his head. He told me that even though they hated each other that Godoi and "Macaco" didn't mind if their students cross trained with each other and even encouraged it.
I found it very interesting, and a bit inspiring, that both of these guys were willing to put their animosity for each other aside in the spirit of wanting their students to excel and get better.
In the end, isn't that what it should be about?