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In a Souslin tree, every antichain is countable, and hence bounded in the tree. Thus, every maximal antichain is refined by a level of the tree. Furthermore, for antichains in $M$, this level by elementarity will be an ordinal in $M$. Since any branch through the tree of height above $\omega_1\cap M$ goes through all such levels, it will therefore meet every such maximal antichain, and hence it will be $M$-generic.