There could be a couple reasons: Two plausible ones were mentioned by Makoto. As we all know, the Sharingan is a pair Dojutsu and so one would need 2 Mangekyou together in order to awaken the Eternal Mangekyou in both of their eyes. The other reason was also stated by Makoto, is because it has been mentioned that the 2 individuals must be related by blood and it makes sense since the only 2 people who have actually ever done this were Sasuke and Madara and they used the Mangekyou's of their siblings.
As for the reason why he did not use his father's Mangekyou, it could be because Itachi knew that he was dying and saw no point in achieving Eternal Mangekyou, just to die to an incurable sickness. He probably knew he wouldn't have enough time to reap the benefits of the Eternal Mangekyou. For more info on his sickness check out this thread; was it ever stated if Itachi was already dying?
The last reason is what I would call "an overwhelming level of Love mixed in with a strong guilty conscience". Itachi wiped out his entire clan to protect Konoha from the coup that the Uchiha were planning, but couldn't kill his brother because he loved him more than everything else. Itachi most definitely knew how terrible his acts were and right from that moment planned to make amends for it by dying at the hands of his kid brother, who would try to avenge the entire clan. Itachi most likely also concluded that Sasuke would have had no chance against him if he had the Eternal Mangekyou, and therefore decided to really fight his younger brother later on after his eyes had deteriorated in such a manner that they would be close in strength and not a one sided battle.
So it was actually because of Sasuke! He knew he was dying and preferred to die at his brothers hand. By doing that, he used his death to make Sasuke stronger. In order to make the fight a bit fair, Itachi decided to let Sasuke have the upper hand (by fighting him while he was partially blind and sick).