Everyone has haters, but there's a difference between a hater and someone who literally just wants you dead. Unfortunately for Arya, the Waif is the latter. Ever since Arya showed up at Braavos the Waif has hated Arya on Game of Thrones. The Waif is a bully in all senses of the word. She constantly questioned Arya's commitment to the Faceless Men, made fun of Arya's life in Winterfell, and then beat Arya up when Arya was blind. In theory the Waif was training Arya to become a Faceless Man, but the Waif also seems to get great pleasure in hurting Arya.
The Waif didn't hesitate to run to Jaqen and let him know that Arya didn't kill that actress like she was supposed to, even reminding Jaqen that he promised she could kill Arya. The Waif was more than delighted when she got the go ahead to kill Arya and Jaqen had to tell her not to let Arya suffer, although it doesn't really seem like the Waif listened to him.
But what is the Waif's problem with Arya? Was she really just worried that Arya wouldn't be completely committed to the Faceless Men (which she wasn't), or is it something else? It's possible that the Waif is at least a little jealous of Arya.
During The Game of Faces, the Waif says she was the daughter of a widowed lord in Westeros who remarried and produced another daughter. Supposedly the Waif's stepmother tried to poison her and that's why the Waif left. However, since the Game of Faces is all about lying, it's unclear how much of the Waif's story is true. Regardless, it's fair to assume that the Waif's upbringing wasn't that great compared to the life Arya had in Winterfell.
The more popular theory right now, however, is that the Waif is actually Arya. Many fans believe this is a Fight Club scenario in which the Waif represents the Faceless Man Arya hopes to be whereas the Arya we've been seeing is her emotional side that's still clinging to the past and Needle. The Waif stabbing "Arya" was really Arya trying to rid herself of her emotional side completely. However, the Waif failed, and thus Arya is still holding onto her emotions and will never really be a Faceless Man.
This theory may seem far-fetched, but the fact that the Waif has really only been seen with Arya and Jaqen makes it just a little bit plausible. Still, this theory seems unlike anything we've seen on Game of Thrones, so it'll be surprising if this is the case.
It does explain, however, why the Waif hates Arya so much. If the Waif really is Arya, then the "Arya" we've been seeing has really been holding the real Arya back. The only way to become the true assassin the Waif/Arya wants to be, is to kill the emotional Arya, and obviously that's easier said than done.