Well, there are different reasons to do the same thing. Some people prefer the meditative side of the MA, especially Tai Chi. Black belts have a higher recognition outside the MA community anyhow.
I suggest you have a calm and collected talk with your parents.
Ask them (in a non whining manner) why they wish for you to participate in the specific MA.
Tell them you wish to do something more self defense oriented, also non bratty in tonation, very important!
Depending on that, you might be able to come to an compromise.
One of the kids in my TKD school also trains in Ninjitsu. We had not discusses the differences in detail, but it's a pretty all inclusive deal, grabs and takedowns in adition to kicks and strikes.
And be asured, even if you can't train in any other MA right now, you are not bound to Tai Chi for life, you can take many more styles in the future!
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