The Church does not teach that our Lady “had to be” sinless, but that it was “fitting” (See
Ineffabilis Deus, para. 2).
As Jharek pointed out, great as our Lady’s dignity is, our Lord’s is infinitely greater; therefore it is appropriate for the Mother of our Lord to receive higher privileges than the mother of our Lady.
Picture the accoutrements the priest uses at Mass. The veil covering the chalice he treats with care, but the chalice with even greater care because of what it contains and comes into contact with.