I'm reading a rather elementary particle physics text, Modern Particle Physics by Thomson. He is staying away from the heavy group theoretic stuff. He derives the transformation law for an SU(2) antiquark doublet and shows it is possible to construct a $\bar 2$ that transforms exactly like the $2$. Then a few pages later, he says there is no way to make a $\bar{3}$ transform like a $3$ in SU(3). The explanation is that it just can't be done. That's obviously not very satisfying, but I image the true explanation is not suited for an undergrad text.
So, what is the real reason we can't create an antiquark triplet that transforms like the quark triplet, i.e. if $q$ is the $3$ and transforms like $$q\longrightarrow q'=\exp(\tfrac{1}{2}i\vec\alpha\cdot\vec\lambda)q$$ then why can't we find a $\bar 3$ $\bar q$ such that $$\bar q\longrightarrow \bar q'=\exp(\tfrac{1}{2}i\vec\alpha\cdot\vec\lambda)\bar q$$