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One should teach the dhamma for the sake of revulsion, of dispassion, of cessation, regarding:
(Nibbidā) Dhamma,kathika Sutta
The above included:
See introduction (Nibbidā) Dhamma,kathika Sutta by Piya Tan
Also the teacher should:
what if I teach the dhamma in a wrong way? Is this causing demerit/bad merit/bad karma?
Yes it would.
What if I mean to teach it in a right way, but it comes out wrong or even causes the listener to have a strong aversion to buddhism/listening to the dhamma?
As long as you have been diligent and taught the right way and tries to correct misunderstanding then what can you do? It is not your fault.
Make sure you do not contribute to the disappearance of the Dhamma. See: Sugata Vinaya Sutta, Candûpama Sutta and others which deal with decline of the Dhamma and impure ways to teach.