Is my answer not good because they fear I leave after a short time?
Unless you are seeking a profession that requires an advanced degree or certification, then - Yes, that is indeed the fear.
Why do recruiters ask this question?
For the same reason. They don't want to present a candidate that turns out to be a short-timer.
When I hire, I am looking for someone for the long term. I invest a lot of time and money while sourcing, hiring, training, and mentoring new workers. I don't want to do that for someone who would be around for a year or so and then leave.
So I talk to new graduate applicants about what they learned in school, where they want to be in the long term, and how they will get there. If I get the sense that what they are saying (without using the exact works) is something like "Well, working here for a while is okay, but I really need to get a graduate degree for what I want, and I'll leave to do that full-time once I save up some money" - then I'm less interested.
If instead they said something like "My long term goals would require me to get an advanced degree - which I plan to do evenings", then I am more interested. I might even start talking about my company's tuition reimbursement benefits, how I attained my Master's degree nights, etc.
So answer the question. And make sure no matter what they you don't sound like you will jump ship soon to get a full-time advanced degree, and you should be fine.