Some people look at the world as it is and ask “why?” Some people look at it as it never was and ask, “why not?”
And some people get pissed off about nearly everything.
Yes, the ordering of the earliest ancestor of our alphabet is either arbitrary, or the reason is not known, and so it might as well be arbitrary.
Can we discuss spelling reform? There is no need for the letter “C”, we have “S” for soft C and “K” for hard C. That leaves C useless. So make C the character to represent the sound we currently represent with the digraph SH.
Also, X is useless. If we want to represent that sound, use “Z” in things like “Xavier”, or “KS” in things like “fox”. Yay, an unused character. It can go back to its original use as “chi” and represent the CH.
Also Q is useless. Let’s use it for ZH–you know, the ZZJJJH sound in “azure” and “pleasure”. I mean, it’s a sound we hardly ever use, but we don’t even have a standard digraph for it, and Q is useless, so there you go.
Aaaand we’re bringing back Þ and Ð for TH and TH.
Plus that upside down e, also known as schwa, that’s every other vowel in dictionary pronunciation keys. You know, ə? How about we use that?
I am equally puzzled.
How would we distinguish ‘Rice’ from ‘Rise’?
How would we spell ‘Cherry?’
In any case, English spelling reform will only make sense in a subset of English dialects, and would be a horrible mess to the others.
Riis and Riiz.
We can handle vowel reform as well. Long vowels and doubled, short vowels are single. Or fuck, we put a hat on long vowels. By the way, “silent e” is hereby abolished. Sorry Tom Lehrer fans.
Xerry. X=Chi.
As long as it works in my dialect–newscaster american english–that is, english the way Jesus spoke it–I’m OK with that. We all have to make sacrifices sometimes. And by “we” I mean “you”.
I have no idea what’s happening.
Yes, it’s annoying as all hell.
Those read as Rees and Reez in my dialect.
Reads as Kzerry.
Exactly 
Spelling reform is like fitting wheels to a tomato.
Many years ago, I was customizing the pronunciation dictionary for the speech board on my wife’s computer. There were some words that it was pronouncing kind of funkily (I couldn’t for the life of me tell you what any of them were, but they may well have been proper names).
Anyway, in the course of my activities, I discovered that given the phonemes necessary to make a speech synthesizer voice the letters “y” and “w,” there is no good reason to consider them to be consonants.
The mystery of why they ARE so designated strikes me as far more compelling than the one in the OP.
Apparently the OP thought he/she had found a way to get the rest of us to recognize the essential arbitrariness of alphabetic order. He/she picked a pair of consecutive letters at random, and in asking us why they are ordered the way they are, hoped we would notice this arbitrariness and comment on it.
Eh, maybe, but I haven’t seen it expressed anywhere else.
I always think people’s voices have colours, but that could be less synaesthesia and more that I watched a lot of TV and played a lot of games with colour-coded subtitles when I was young 
Yes, I guess that’s sort of the idea. I apologize for being oblique.
But for me a larger theme is that we often just assume that the things we take for granted have some kind of well-reasoned basis, when they don’t, and alphabetical collocation is one of the most ubiquitous systems by which we organize ourselves. The G things are always coming before the H things, but there’s no natural basis for it. Lexical collocation is kind of the same, but it’s one of the most fundamental ways that we “sense” native-like use of language.
Are we to learn something from this, then?
And yet, your OP had the effect of making it look like you were the one person who didn’t just recognize that it was arbitrary, with your insistence that G before H was a “mistake”.
Probably not, but feel free to ridicule the whole notion, if you wish.
Guizot: why does g come before h?
Everybody else: no reason, it’s arbitrary.
Guizot: seems to me there’s a reason.
Everybody else: nope it’s just arbitrary.
Guizot: gotcha! I was just trying to show you how arbitrary it is!
They are called consonants because people are to lazy to extend the classification of letters. ‘w’ is a full semi-vowel, in that its only real functions WRT enunciation are to modify the attack of a vowel and to form true diphthongs (where it precedes ‘r’, it is basically just a silent appendage). ‘y’ is a full semi-vowel that can also stand alone as a vowel. ‘h’ is a partial semi-vowel (it does not really form true diphthongs that significant modify vowel sounds) and a lenition adjunct (where it modifies consonant sounds). ‘g’ also lenites ‘n’ to form a sound that kind of blends the two but it not really derivative of either. Some even go so far as to classify ‘r’ as a semi-vowel, though, like ‘h’, it does not significantly modify the preceding vowel (in non-rhotic dialects). Then we come to the ‘dark l’, at which point, if you were not already, you start screaming for me to stop.
Because there’s no such thing as a scary hgost story.
Please account for the following in your OP then.
Satire.
Next time I promise to put in a smiley face.