Is there a stigma of assigning the title TA to an undergraduate?

A teaching assistantship (TA) is a formal job category at most universities, which implies that you are being paid a specific wage for teaching duties while a graduate student. Consequently, you would be misrepresenting your work on the CV if you called yourself a teaching assistant, because you are not formally a graduate student.

At the university level, another issue may be that while many undergraduates do participate in teaching responsibilities at many schools, this is often in the form of tutoring programs and informal arrangements. Part of the reason for this is that many universities want to be able to claim a higher percentage of teaching duties are done by faculty than is really the case. Calling undergraduates graders and tutors helps to shift off the balance, since they are not officially "teaching staff," and therefore wouldn't be included in such time accounting.

In my experience, the answer is: teaching assistantship (TA) is a formal job category at most universities, which entails a specific combination of job duties. Those job duties go beyond what you are doing. Therefore, you would be misrepresenting your work on your CV if you called yourself a TA, because you have not been formally appointed as a TA (and because a TA would be expected to take on additional duties beyond what you have been doing).

Note that this is a little different from aeismail's answer. In many institutions, undergrads can be appointed as a TA, under certain circumstances. That doesn't mean that you can just call yourself a TA if you feel like it. For instance, assisting informally or helping with grading papers doesn't necessarily make you a TA; it's not unusual to hire undergraduates to help with those tasks, under some other job title -- but not as a TA. A TA is a very specific job title, and unless you've been appointed under that job title, you should not call yourself a TA.

And I think you're misinterpreting the situation, when you presume there is a stigma against hiring undergrads as a TA. I suspect it's more likely that there is a different explanation: that your instructor reacted negatively because you were proposing to describe yourself as a TA when you have not actually been formally appointed as a TA.