I feel like it's because his body is shutting down in a way since in the earlier chapters we see that sihwas mother(alien) said that sihwa would be killed/destroyed once they return to planet alpha. I think it also mentioned how he was a failed experiment.
Ok my only two thoughts are he coughed up blood because….
A. Earth is making him sick so he needs to be taken back to his home planet
Or
B. He has whatever sickness his father had before he passed (but idk if that’s possible)