Which is more likely to cause a delay in teeth growth: health problem or is it a symptom of a psychological issue?

Genetics. Genetics play a very large part in the eruption pattern and timing of the transition between primary and secondary teeth. Since there is a wide range in this timing, what you might consider delayed may well be within normal limits. Discuss this with your dentist or the child's pediatrician.
Medical problem. I know of no instances where a psychological issue has interfered with the growth and development and eruption of teeth. Might want to check with the psychology/psychiatry experts on this.