By the FKG inequality for FK-percolation, the probability of the alternating two-arm event is smaller than the product of the probabilities of having a primal arm and a dual arm, respectively. In this paper, we improve this inequality by a polynomial factor for critical planar FK-percolation in the continuous phase transition regime ($1 \leq q \leq 4$). In particular, we prove that if the alternating two-arm exponent $α_{01}$ and the one-arm exponents $α_0$ and $α_1$ exist, then they satisfy the strict inequality $α_{01} > α_0 + α_1$. The question was formulated by Garban and Steif in the context of exceptional times and was brought to our attention by Radhakrishnan and Tassion, who obtained the same result for planar Bernoulli percolation through different methods.