Do you think it is wrong for a student to train in two dojangs? Is it considered disloyal to the present master? Do masters mind if their students train elsewhere?
Everyone is insecure in some way, instructors included. Some are afraid that if students visit other schools, they may find that they (the current instructors) do not know what they are doing, they may fear the students may think the other instructors are better than they are, they may fear the students will like the other martial arts better than Taekwondo, or they may fear the students may change schools.
Masters who think their students would never want to visit another school must have slaves for students. It they have free thinking, inquisitive students, then the students will get curious at some point and want to check out other styles. Masters who fear this have too much insecurity. Just as parents raise their children to leave home and make it in the world, instructors should be happy when their students leave home and keep growing in the martial arts. No matter have knowledgeable the instructor, at some point, he or she will have taught a student all he or she knows. At this point, the instructor should encourage the student to further his or her knowledge in other arts. It may not be best for the business, but it is best for the student.
Training in two dissimilar arts, such as Taekwondo and Judo, is usually not a problem. The two arts use different techniques. However, training in two similar arts, such as Taekwondo and karate may be a problem. They both use stances, punching, and kicking techniques, but the manner of performing the techniques may be very different. A Formula 1 race car driver may also race a fuel dragster and be a champion at both, since the driving techniques used in each are different. However, while a Formula 1 race car driver may learn to race a NASCAR stock car, the driver cannot race both and ever expect to win at either. The driving techniques are very similar in each, but the intricacies that make one a good driver in each are very different.