If he loved Izuna so much, why did he stab Sasuke?
He was drawing a parallel to illustrate how, in Hashirama's world of cruel paradoxes, shinobi are forced to sacrifice something to protect something else. To protect his current dream, Madara was willing to go as far as Hashirama went in the past, killing whoever got in the way of that dream, be they "friend, brother, or even my very own child." Madara felt a kinship with Sasuke; intuitively, Sasuke was something between a brother and a child to Madara, simply due to Sasuke's similar life path and all of the things Sasuke represented.
Madara would never have killed Izuna. At the time that Madara first heard Hashirama utter those words, Madara warned that Hashirama had his priorities backwards, and that the contradiction would lead to darkness. In the end, by stabbing Sasuke, Madara was embracing that darkness as an inevitability of Hashirama's world, but it was a bitter moment.