Sure thing! Might get a little long-winded, though, but I’m gonna be a little detailed. TL;DR at the bottom, though, I don’t wanna waste your time.
The Tumblr fanbases of both of these shows, and even quite a few folks over on Twitter, both see these as two differently written trans allegories. Neither was intentional, but that doesn’t necessarily mean it isn’t there.
My Life As A Teenage Robot starred a main character constantly dealing with a parent trying their best to sequester them off into an identity they did not agree with, even going so far as to change their name and try to publicly portray themselves as their chosen identity rather than the one given to them at “birth”. One of the key things that happens quite a lot? The “Jenny” vs. “XJ-9″ argument held constantly in the show between mother and daughter. A lot of people see this as an allegory for publicly transitioning as trans, especially with the “dead name vs. chosen name” arguments in-show, and while the creator did not intend for this, they have gone on record saying they could easily see how this could’ve been seen and are happy as could be that people are finding their own meaning in a work to help their own struggles feel easier and more visible, as seen here:
That’s what “death of the author” is: it isn’t just removing the context of the given piece of media, it’s finding your own meaning in something even if it was not the intention, and ultimately it’s your own personally found meaning in a work that’s more important than what was ultimately intended: a fun, quirky, stylish show about a robot kicking alien butt while trying to fit in with humans. As Rob put it? “Art is open to the audience’s interpretation.”
Which brings us to Danny Phantom. Arguably the same basic premise (a high schooler fighting against an invading threat while trying their best to fit in with friends and family), but done differently: Danny hides his powers to a point where many fans have seen this in the light of this being an allegory for being in the closet. And because his powers have to do with transformation, the fanbase has latched onto him being trans in the closet. Which makes sense, many trans people have family that have been extraordinarily vocal in their displeasure with the “special snowflakes” and “fake identities” they view as a threat or morally wrong. Look at Danny’s parents: his second identity is as a ghost, and they hunt ghosts with enough vigor that they gleefully show off how deadly and effective all their inventions are.
Butch Hartman, creator of Danny Phantom, has gone on record either denying or skirting the issue entirely when pressed about this allegory. And his response has been to push as many “Christian Value” stunts as he could with a lot of thinly veiled “family-friendly” stunts that, to the trained eye, look a lot like something lgbt-phobic folks will hide behind to push bigotry. I’d link his Kickstarter that’s been completely radio silent for an entire year or quite a few videos detailing his… many responses to the theories and allegories, but I want this to be clear: he does not believe it exists, and thinks that his word is law as the creator.
All you have to do is search “danny phantom trans” to see at least the lighter side of all the many, MANY theories detailing the allegory, though (searching “my life as a teenage robot trans” leads you to the exact tweet I screenshotted up above, too!). So despite what Butch has tried quite hard to not sound like a complete asshole about denying? The community, despite not everyone believing it, highly favors this theory due to the many parts of it that lead to the conclusion. Again: death of the author. Art is open to the audience’s interpretation.
TL;DR: Basically put? The above posts are from those in the fandoms of those shows that see a trans allegory in their texts. The creator of My Life as a Teenage Robot embraces this. The creator of Danny Phantom most assuredly does not.
But both are valid, because what the audience takes from art is the most important part of consuming it.
