In context of the quote, I was quoting to my mom. If she has no problem with it, I'm fine with it.
Everybody who reads knows you were quoting to your mom. The issue is what were you trying to say when you quoted the proverb to your mom ? Nobody is interested whether at the end of the day your mom has problem with your moustache or not. It's the meaning of the Chinese proverb used in that context that is the subject.
My mom keeps nagging at me to shave it off. I rebutted, 身体肤发,受之父母,i.e. mom, you gave that to me.
In your own words, clearly your mom was not okay with your keeping the moustache...in your own words, she wanted you to 'shave it off'.
And the Chinese proverb, in your own words, were aimed as a 'rebuttal', implying that because it was given by your parents and that you had a moral obligation to protect whatever was given. That was your reason for not shaving it off.
In other words, you're suggesting that because it was given by your parent shaving it off would be morally wrong. In the same context, are you going to keep your hair ? Are you going to keep your nails ?
In order to answer this question, one must understand the context of this proverb - the original context. The full version is:
身体发肤,受之父母,不敢毁伤,孝之始也
This brings us to Spock's explanation, that it's used in the context of 'inflicting harm to one's body' is a breach of filial piety. The full version clearly says so.
So your rebuttal carries the implication that shaving your moustache means inflicting harm to your body, and for the sake of filial piety not only must you not shave it, it's a reason for you to keep it.
If shaving moustache is inflicting bodily harm on oneself, and if that sounds ridiculous to you, then Spock is right that you used the Chinese proverb wrongly. At this point, we're not even into the topic of tattoo.
The issue of tattooing is not about whether your act of shaving tantamount to inflicting bodily harm. The issue of tattooing was raised to highlight the 'awareness' over relative opinions on what amounts to inflicting bodily harm, not whether 'shaving amounts to inflicting bodily harm.'