The most probable explanation for why there are many endemic plants and birds in New Zealand, but no native mammals, is:
Plants and birds would make ocean crossings to the isolated New Zealand islands, mammals could not.
Mammals generally require more specific conditions for survival, and their ability to cross large bodies of water is limited compared to birds and plants, which can disperse through various means. Birds can fly short distances over water, and plants are capable of being carried by wind or water currents. This has allowed birds and plants to colonize New Zealand more successfully than mammals.