e.g. arraylist: [ ]
Even though there is space left in the array, we still need to move all the values one index to the right to be able to insert at the front, which takes O(n) time. In contrast, inserting at the front of a linked list is simply a matter of moving pointers and therefore constant time.
But it is helpful to keep the terminology clear, because an insert in the middle of a linked list is still O(1), but inserting into the middle of an array will require moving some fraction of the data.
The OP is discussing inserts at the start just because it is the worst-case scenario for arrays, then a positive result will still be true if some of the inserts are in the midddle or even near the end.
This is true if you already have a reference to the middle of the list. If you don't (say, because you want to insert while preserving the fact that the list is sorted), then inserting into a linked list is O(n) just like the array is.
If you give metrics for the case that should be worst for your argument, people give you shit about using such a stupid example.
There's no way to avoid someone giving you grief no matter what you do.