The unintuitive step is apparently identifying the index with the cardinality of the collection from before the item arrives, not after it arrives – i.e. ‘the n-th element is the one that arrived after I had n elements’, not ‘the n-th element is the one such that I had n elements after it arrived’. The former identification results in 0-based ordinals, the latter leads to 1-based ordinals – and to some misconceptions about infinity, such as imagining an element ‘at index infinity’ in an infinite list, where no such need to exist.
It's only an ordinal because we've confused ourselves into saying it can be. It's the same situation as with starting to count from zero in most programming languages, and from the wikipedia page for "0th", it appears to actually be the effect of an influence of those artificial language choices onto the mathematical concept of ordinal. After all, it is in the end just a convention, and we could start calling the first element of a sequence "the zeroth" instead, but there would be no benefit for it at the language level - which is where it matters. These artificial languages we're creating should try to mold themselves to how we already use language, but the opposte is what's been happening to some degree.
The unintuitive step is apparently identifying the index with the cardinality of the collection from before the item arrives, not after it arrives – i.e. ‘the n-th element is the one that arrived after I had n elements’, not ‘the n-th element is the one such that I had n elements after it arrived’. The former identification results in 0-based ordinals, the latter leads to 1-based ordinals – and to some misconceptions about infinity, such as imagining an element ‘at index infinity’ in an infinite list, where no such need to exist.