I don't have a problem with the game as a concept. It's basically a reskin of Triple Triad from Final Fantasy VIII. The execution is another matter, however. It runs painfully slow, you start with a pitiful card pool, and you only get one new (scripted) card per opponent (and they aren't much better than the cards you started with), meaning there's no reason to replay anyone after the first time, etc.
If I had to identify the two worst problems, it'd be that you don't get to pick a card to strengthen your deck, and that your opponents have a limited deck themselves. Combined, these two things both prevent the game from being rewarding, and prevent it from being surprising. You basically just save scum your way to victory. By changing both of these things, the game would have better progression and feel more rewarding to play. Maybe do something like give the opponents ~20 cards to construct a deck out of. These 20 cards don't all have to be different mind you, with duplicates being weaker or stronger depending on how strong the opponent is supposed to be, since that increases the likelihood of drawing that particular card being drawn.