Political discourse on social media has grown increasingly toxic, with electoral periods amplifying partisan hostility and cross-group attacks. Yet it remains unclear whether toxicity in online political speech reflects how partisans communicate within their own circles, or how aggressively they engage with the opposition. Disentangling these dynamics is critical for understanding online political hostility and for designing effective content moderation. We examine this question at scale using a large collection of original posts and replies from X (formerly Twitter), collected during the 2024 U.S. presidential election. Using a human-validated large language model to classify the political alignment of posts and users, and the Perspective API for toxicity scoring, we uncover a striking asymmetry: Republican-leaning posts are significantly more toxic than Democratic-leaning posts, yet Democratic-leaning posts attract significantly more toxic replies. To interpret this finding, we compare the toxicity of same-party and cross-partisan replies. While cross-partisan replies are slightly but significantly more toxic than same-party replies, this is true for both Democratic and Republican posts. However, Republican users account for a large majority of replies to Democratic posts, while Democrats account for a minority of replies to Republican content. Therefore, the elevated toxicity directed at Democratic content is better explained by the volume of Republican cross-partisan replies.