The only reason that "an" exists is that there are words that start with a similar sound to "a." If you were to say "I want a apple" at a conversational speed, it would sound like "I want apple." It sounds like you aren't using the article "a." As far as I know, no one denies that this is the reason for the existence of "an." That extra letter N helps us understand that a speaker is using the article "a"
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Now lets move to SLP. It starts with an S. Why does it sound better with an "an"? Well, because S doesn't start with S. S starts with "eh" Two parts: "eh" and "s". S So you could say "I'm a speech therapist," or you could say "I'm an SLP." Personally, I wouldn't say or write "I'm a SLP." Even when I do say it, I tend to put a little pause (glottal stop) between a and SLP. Another example might be university. You wouldn't say an university. It's a university. Because university starts with the y sound, which is a consonant.
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Spanish has similar rules. If you use o (or in English) before a word that starts with o, you change it to u. Agua is feminine, but the water is "el agua" because if you were to say "la agua," it would sound like one word.
In the modern world, language takes oral and written forms. An SLP sounds better, while a SLP may be said to look better. The written form is a reflection of the oral form, and in my opinion, should follow changes in the oral form.
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As far as "An history", this clearly breaks the "Use 'an' only before vowels" rule. I'm not sure how it gets justified, and I don't really care. As far as I'm concerned, it's "a history," and others can do what they want. At the end of the day, the purpose of language is almost always communication, and either form communicates the information.