The whole statement in the Talmud in context, Maseches Shabbos 118b, is:
א"ר יוסי יהא חלקי מגומרי הלל בכל יום איני והאמר מר הקורא הלל בכל יום הרי זה מחרף ומגדף כי קאמרינן בפסוקי דזמרא
Rabbi Yosi says "Let my portion be among those who complete Hallel every single day." This can't be, doesn't Master say "One who reads Hallel every day - this is a [heretic]" When we said [the first statement] it was referring to Pseukei d'Zimra.
Rashi says the issue is that Hallel was specifically enacted at a specific time, and by saying it all the time one is turning it into a song, not a prayer. Contrasting that with Pesukei DeZimra which was established to be said every day, it doesn't have this issue.
The Shiloh (towards the end of עניני תפילה וקריאה בספר תורה) brings Rashi, and also quotes Rabbeinu Yona who brings an opinion that the issue is saying the Bracha on Hallel, but Rabbeinu Yona rejects this by saying that the statement in the Talmud includes when a Bracha is not said and instead explains that Hallel is said so that no harm should befall the congregation by invoking the miracles of the Exodus. We say Hallel at times that remember when such events occurred. By saying it every day one is implying that Hashem does not perform daily miracles and one needs to invoke the miracles of the Exodus instead. Whereas Ashrei invokes the daily miracles and should be said every day - one who does is guaranteed a place in the world to come.
The Shiloh then quotes the Yerushalmi which says that Hallel references idols of silver and gold. By saying it every day it is like mocking Hashem that He cannot get rid of them.
The Shiloh then gives his own answer - Hallel is said at times when we remember the Exodus, and thus is appropriate when associated with the Exodus to commemorate the miracle (it is said on Rosh Chodesh because Rosh Chodesh establishes the day of the holidays). However, by saying it every day it would imply that there is something essential and defining about G-d in the miracles that he did with the Exodus, which violates the idea that G-d is פשוט תכלית הפשיטות - completely without form or definition.