Proficiency in teaching Dhamma

The more insight one gains by meditation and studying the suttas, does one also gain a higher proficiency in teaching the dhamma? To put up an extreme example, if someone attains nirvana/full enlightenment, is he as proficient/competent in teaching the dhamma as the Buddha himself was? I read that there can be Buddhas, which attain enlightenment by themselves, but neither have the fellowship nor the necessary skill to teach the dhamma, is this true?