In an effort to understand your post, I ran those through the English Wiktionary which some may not know, also has foreign words.
αιτιολογώ: https://en.wiktionary.org/wiki/%CE%B1%CE%B9%CF%84%CE%B9%CE%B...
δικαιολογία: https://en.wiktionary.org/wiki/%CE%B4%CE%B9%CE%BA%CE%B1%CE%B...
My personal interpretation is that this like the difference between an explanation and an excuse, but perhaps someone here has a better interpretation.
So this is purely causal without imposing the person’s subjective judgement onto the action or event; simply expressing that given the circumstances, it makes sense that the events occurred, whether the person was right or justified in acting as they did is a different story. So given the events I can reason why the action occurred.
For δικαιολογία / δικαιολογώ, the words are derived from δίκαιο and λόγος again; the former meaning the person is in the right, or is morally correct from the perspective of the person expressing it. Thus, justifying is closer to δικαιολογώ.
For an example; chores are boring, so I didn’t do them even though I promised I would. You can reason why I didn’t do them but you can’t claim I was justified in not doing them. I promised I would and breaking promises is generally immoral without s good justification or a reason.
Separately I like the phrase "a reason is not an excuse" quite a lot. I can empathise with people who make terrible decisions and understand their reasoning, but that doesn't make me excuse the choices that they made.
Unfortunately the brain is rather complex and can break in surprisingly many ways. One such example is the shooter who had cancer that pressed against his [iirc] amygdala.
For Ted, we know that he was a subject of mkultra experiments, and that he was tortured. We know that he was deeply troubled and had communication issues. Perhaps he felt that the bombings were the only way he could garner focus on the problems he saw; but that is likely rationalisation on my end. It should also be noted that Ted lived very isolated, and that can cause severe damage to the brain. If you find yourself alone in a foreign country that you work in and no social support system or many interactions, you might experience this and see yourself changing.
In Greek αιτιολογώ and δικαιολογώ exist, where the former identifies causality and uses that to reason on the events and the latter is the same as justifying. To my knowledge the former doesn’t have a translation in English.