According to the story, Jayadratha encashed a boon granted by Lord Shiva, where he can hold back all the Pãndavas except Arjuna for a whole day during war. Thus, during the 13th day of the war he became indirectly responsible as he stopped all Pãndavas (except Arjuna and Lord Krishna), when Abhimanyu was being slain by multiple Kaurava warriors in a deceitful way.
However, it's important to note that Jayadratha was neither present during Abhimanyu's death nor did he participate in the cheating. In fact, attacking the lone son of Arjuna was decided on the spot observing his invincibility.
Later on, instead of taking an oath to kill the Kaurava warriors most responsible for Abhimanyu's death, Arjuna went for "Mission Jayadratha"! Had he failed, he would have burned himself on the battlefield in front of all the warriors.
What wrong did Jayadratha do to face the wrath and animosity from Arjuna? Or was it just pure emotions which led Arjuna to take such an unwanted risk?
Side question: Before Jayadratha's death, there was a Solar eclipse in the sky to make it dark, which resulted temporarily in declaring end of the day. How long did the Solar eclipse (dark) last?