The Gemara advises one to instruct his household gently ‘so that they accept from him’. The Rosh cites the Gemara (Gittin 6b) that a person should never instill excessive fear in his home. This reason would indeed seem a sufficient basis for our Gemara as well; why does the Gemara provide the reason of ‘acceptance’ instead?
The Gemara in Gittin actually brings our Gemara as well, after mentioning the above-quoted statement. Not being gentle doesn’t necessarily equal excessive fear. So the Gemara there is bringing two levels. First, that you should not instill excessive fear. And second, that you should speak gently so as to have your words accepted.
Moreover, here we are talking about Mitzvos. It is not simply barking orders and demanding having things your way. If you are a Yarei Shamayim, you are actually worried that the Mitzvos be done correctly. Nevertheless, we are told to speak gently and hide the urgency, so that your words are accepted.