It is difficult to rationslise the て-form of Japanese verbs in the mind of a speaker of an Indoeuropean language because there isn't something directly equivalent. However, it's been a few years now that this concept popped into my head that there is an implied meaning within the て-form as meaning "in the state/condition/form of". This to me makes sense with the te iru structure:
私はリンゴを食べている Literally: I exist in the state of eating an apple.
I just wanted to see if this thought goes in the correct direction in relation to the て-form.