First of all, as Outhra notes, the term appears alongside "Lust-object" in the PPC Agents infobox, which is usually what people are looking at when this question comes up. I put that space in the infobox myself, so I can tell you with certainty it's there to cover anyone (and anything) an agent might have strong protective feelings about in addition to the characters they lust after—if any. Not everyone HAS to lust. Why should they? However, everyone has favorite characters, or species, or languages, or places, etc. "Favorites" provides a space for that. It doesn't replace the space for the character(s) an agent actually does lust after.

Second, when were people complaining about saying "Lust Object"? I don't remember this. Admittedly, that doesn't mean much, but usually I notice if there's a widespread movement to change something about the PPC.

~Neshomeh

The wiki's Agent templates show both, one right under the other, and it's not hard to see where there might be confusion.

eatpraylove, I that the distinction is in the way they are viewed by the agents. A Lust Object would be someone who an individual agent finds extremely attractive, and depending on the agent, that lust could go to the extent that any mission involving that character could potentially be compromised. That's why one needs to register one's Lust Objects with the Department of Personnel, so that they can assign missions with a registered Lust Object in a primary role to someone else, assign them to you with a fair deal of warning, or assign them to you because there was a filing error or they/the Ironic Overpower thought it would be funny.

Favorites are more like characters that the agent in question particularly enjoys within canonical material. An agent would react more strongly if a favorite character was altered by a badfic and driven to uncharacteristic acts, because they have a stronger investment in that character. Maybe, in a badfic, someone who is usually very humorous would start spewing the worst jokes or angsting in a corner, or the wise swordfighting mentor would make rudimentary battle mistakes. Even if they're not someone's favorite, it would be a charge either way, but if they are, the agent might start an angry rant or begin banging their head against nearby objects, or with the worst cases/with the most rage-prone agents, need to restrain themselves from going up and indignantly decking the replacement right in the face, which would reveal the PPC's presence too early.