What is meant when one tells someone that they are beautiful on the inside? Generally, it is intended to say "You're a good person on the inside, so your outwards ugliness isn't important." That is, in of itself, a far better than "You're beautiful on the inside", so what is wrong with "You're beautiful on the inside" that isn't about its meaning? Quite simply, it equates "good" with "beautiful." Imagine, for a second, that the scenario is different. Rather than speaking to a ugly person, one is speaking to a black person. Would it be ok for one to say "You're white on the inside," and mean it as "You're a good person on the inside"? No, it wouldn't be. This is, fundamentally, a myth. Beauty does not indicate goodness and goodness doesn't necessitate beauty. When one who believes this myth, be it consciously or subconsciously, ans one encounters a good ugly person, this can be resolved three ways. First by rejecting the goodness of the ugly person. Second, by rejecting the myth itself. Third, by creating an inner beauty. This is fundamentally no different from the attitude of many Southerners in pre-Civil War America that, while black people, in general, are bad, specific black people they care about, like their Nana or favoured servant are exceptions, oftentimes using the same sort of language, calling them white "on the inside".
However, the problems with the phase run deeper. Consider a moment the meaning, "You're a good person on the inside, so you're outward ugliness isn't important." Within this meaning lies the same problem. It sees ugliness as something that's bad, and is overcome only because of the inward goodness. We must not merely remove our language from the myth, but our meaning.
In the language and meaning of the phrase, it supports oppressive myths, though often involuntarily. Oppression isn't always intended, and usually unwanted, yet many still support oppressive institutions in their speech and actions. They don't intend it, but that doesn't reduce the harm. Consider, for a moment, right-libertarian support for wage slavery and capitalism. They aren't intending to support oppression. They don't see the oppression in their actions at all. To them, it isn't oppressive because it is voluntary and contractual. However, this misses the oppression in the inequality. The boss can order around the worker just as the slave owner could order around the slave or the boss could order around the indentured servant. This oppression is not eliminated by making it voluntary.
So, having established the problems with the phrase, what are some alternatives? I mean, I don't deny that some people are helped by the phrase in individual cases, even if the phrase is a part of the societal problems that caused the problems, so we need an alternative to help them. One method would be to tell them that a lack of beauty doesn't make them a bad person and doesn't prevent everyone from seeing the goodness inside of them. Going off of that, one can show how you care for them, but not in spite of their ugliness. Rather, you care about them because of what sort of person they are and their outward looks aren't important to that.
I'm sure there are other methods, and, if you have suggestions, feel free to say so in the comments and describe your alternative.