After Mitsuhide defeated Nobunaga, he chased and killed his son, Nobutada, who would of had claim to the leadership. Why did he not chase after Nobunaga's other sons? Would they not of had claim to the leadership, or was it due to time constraints and maybe not enough military power?
Mitsuhide went after Nobutada because, like Nobunaga, Nobutada was in Kyōto with a small entourage. It was an opportunity. In comparison:
Nobunaga had younger sons who were not yet adult and their locations at the time are uncertain. But it doesn't really matter. Nobunaga's adult sons who didn't die on Tenshō 10.VI.2 were far away and with significant forces. In the 11 days between Honnōji and Yamazaki, Mitsuhide was busy trying to conquer Ōmi and convince the lords to Kinai to side with him (to no avail).
Hey there,
Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.
If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!