The first card the woman flips over must always be a new card, because she hasn't seen any before. The second card can either be another new card, or the match to the first card. Obviously the latter is not ideal for making it take the longest possible amount of turns, so it's then another new card.
From every turn after this point, if the first card flipped over is one that was previously seen, then she will match it, so the man has to avoid this if possible. The second card will end the turn whether it is a new card or one that was previously seen, so ideally he will make it an previously seen card because not only will she still have to spend another turn matching that card regardless of when it turns up (as long as it's not the match of the card that was also turned over this turn), but also the pool of cards she will be unable to match if they turn up will stay as high as possible.
So the end result is something like this:
Turn 1: 2 new cards (2 unmatched, 50 unknown)
Turn 2: 1 new card, one old card (1 potential pair, 2 unmatched, 48 unknown) -One of the flipped cards, becomes an unmatched, and the second card turns itself and one of the unmatched into a potential pair
Turn 3: Match old cards (1 pair, 2 unmatched, 48 unknown)
Turn 4: 1 new card, one old card (1 pair, 1 potential pair, 2 unmatched, 46 unknown)
Turn 5: Match old cards (2 pairs, 2 unmatched, 46 unknown)
-Repeating this pattern, on average one new card is revealed each turn, and one match is made every other turn. This suggests it takes as many turns as there are cards to finish, but because the first turn is an exception to the pattern and revealed two new cards, the highest possible amount of moves is one less than that. So it will continue on until:
Turn 46: 1 new card, one old card (22 pairs, 1 potential pair, 2 unmatched, 4 unknown)
Turn 47: Match old cards (23 pairs, 2 unmatched, 4 unknown)
Turn 48: 1 new card, one old card (23 pairs, 1 potential pair, 2 unmatched, 2 unknown)
Turn 49: Match old cards (24 pairs, 2 unmatched, 2 unknown)
Turn 50: There's only two cards left, so this must turn over an old card. Match it (25 pairs, 1 unmatched, 1 unknown)
Turn 51: Last card must be an old card. Match it (26 pairs)