There are many instances in Undertale when certain words or phrases are highlighted in certain colors. Red is used more frequently than most of the other colors, excluding yellow, and also appears to have a theme attached to it.

-Toriel says “ASGORE” and “ruins” in red text

-Papyrus says “ultimate feelings”, “dating/friendship hud”, “hidden power” “my secret” and “phone number” in red text

-Alphys uses red text when talking about her date with Undyne

-Apparently Mettaton says “I am Mettaton, big time sexy robot lover” in red text (which is not used in game)

Aside from these instances, red text is primarily used by Chara in the no mercy route.

At Home:

- “Where are the knives?”

At New Home:

- “He leaves them in the kitchen and the hallway.”

- “There are two keys.”

- “I unlocked the chain.”

- “No chocolate.”

- “Nothing useful.”

- “Still has that sweater.”

- “My drawing.”

- “…” (when looking at the family photo)

- “The date I came here.”

Other:

- “Strongly felt ________ left. Shouldn’t proceed yet.”

- “That comedian.”

- “____ left.” (Amount of monsters still alive)

Based on this information, I feel that red text is used to highlight something the speaker feels very strongly about.

- Toriel feels strongly about Asgore because of how he declared war on humanity and killed six children, and feels strongly about the ruins because that is the place she locked herself up after leaving Asgore.

- Papyrus feels strongly about all the things he mentions during his date.

- Alphys feels strongly about her date with Undyne.

-Mettaton must feel strongly about being a “big time sexy robot lover”.

-Chara feels strongly about a lot of the aspects of their old life.

-Chara literally says “strongly felt” when warning the player not to proceed.

So, going off the conclusion that red text is used to highlight things that the speaker feels very strongly about, what about this:

The narrator is the speaker, and the word that is highlighted in red is “Hole”.

Now, who likely has a strong feeling toward holes?

Chara.

___________________

Sources:

http://doge-w-a-bloge.tumblr.com/post/131441098980/all-red-asterisk-text-in-the-game-data

https://m.reddit.com/r/Undertale/comments/48rf2j/summary_of_how_colors_are_used_in_text_spoilers/

(submitted by anonymous)