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We prove failure of the natural formulation of a matrix weighted bilinearCarleson embedding theorem, featuring a matrix valued Carleson sequence as wellas products of norms for the embedding. We show that assuming an A2 weight isalso not sufficient. Indeed, a uniform bound on the conditioning number of thematrix weight is necessary and sufficient to get the bilinear embedding. Weshow that any improvement of a recent matrix weighted bilinear embedding,featuring a scalar Carleson sequence and inner products instead of norms mustfail. In particular, replacing the scalar sequence by a matrix sequence resultsin failure even when maintaining the formulation using inner products. Anyformulation using norms, even in the presence of a scalar Carleson sequencemust fail. As a positive result, we prove the so called matrix weightedredundancy condition in full generality.

Failure of the matrix weighted bilinear Carleson embedding theorem