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One of the big reason is matching like genrally we do in (a^n b^n ) and push and pop does it in O(1)
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In stack we do all operations at the top of the stack.
We push at the top, we pop from the top.
So we do not need any move operation in stack to compare anything.
To accept CFL, we need something like this.

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PDA has been defined using stack. Although We can implement using different data structures but if power of Automata’s acceptance increases or decrease we may have to put it in different class of Languages i.e it may or may not be CFL anymore.

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