When people tried to “axe” me something, I used to say “God, no! Please don’t axe me!” But nobody got the joke, so now I just let it slide.
My mom, who in most cases is a stickler for pronunciation, drives me nuts with this: she pronounces “leash” (as in what you use to walk a dog) as “lish” (rhymes with “dish”). I stopped correcting her many years ago because she honestly cannot hear the difference in the two sounds. She’s from Hamilton, OH.
Theng? I don’t know if I’ve ever heard anyone pronounce ‘thing’ this way. ‘Thing’ yes, ‘thang’ sometimes, but only when I travel to the South, and even then very infrequently, but ‘theng’? Do you pronounce ‘king’ as ‘keng’ or ‘bring’ as ‘breng’ as well?
I’ve heard others claim that they don’t hear the difference between the proper pronunciation of a word and how they pronounce it. I can (somewhat) understand getting into a habit of pronouncing a word differently than the standard, but I can’t wrap my brain around when someone says they can’t even hear the difference between the two.
For example, ‘wheel’ and ‘will’ are not homonyms, but I’ve been told by someone that they sound exactly alike to them, and they pronounce them both kind of like ‘wiuhl’. What I don’t understand, however, is they claim they don’t hear the difference even when I pronounce the words in front of them. How is that even possible?
I don’t get it, either, but I’ve encountered this phenomenon on several occasions. I wonder if there is a physiological explanation-- something akin to being tone deaf or color blind?
Maybe they still need to differentiate between present and past tense of a verb?
Good try, though. This transposition of sounds (called metathesis) is a common, natural, and perfectly logical phonological phenomenon. That is to say, it’s not just “sloppy” speech. Some people, who apparently have no problem when it happens with words like prescription, totally freak out when they hear it in ask. It’s good to see someone approach it with some humor.
I’m afraid I did this all the time in high school German. The teacher would say something, I would repeat it, he would try to correct me, and I couldn’t really hear the difference between what I was saying and what he was saying, although I’m sure the poor man was cringing inside. We would go to the language lab, and I would think I was repeating correctly, but I wasn’t. I really couldn’t hear a difference. I don’t know what it’s called, but I had it.
I think it’s probably not necessary for me to confess that if something like this exists, I probably have it. Like Pai325 described, my attempts at learning foreign languages have been disastrous. Reading and writing are fine, but trying to mimic pronunciations is very, very difficult.
I asked a bunch of people to say “thing” for me yesterday. It sounds like “thang” or “theng” to me. Also, upon reflection, I’m pretty sure that the reason I don’t think “something” rhymes with “thing” is because I say “sumthin”. Awesome. Maybe I am Larry the Cable Guy. 
This is where foreign accents come from, IIRC. When you learn a language young you learn certain phonemes. If a phoneme isn’t used in your language, you don’t learn it, and it’s indistinguishable from other similar phonemes you do know, but people who do know it will hear the difference. I can sometimes hear those differences if I listen really closely, but not always. If when learning a language, I was having trouble distinguishing between similar unfamiliar and familiar phonemes, I would want to know tongue, lip, and teeth positions of the troublesome word. Different languages, like foods, have different mouth feels.
I just realized that for me, thing and something don’t usually rhyme. Add an “ing” to most verbs or gerunds and I don’t usually pronounce the final g. Something has that form even though it isn’t actually, so I lose the final g too.
Michigan here.
Thing and sing rhyme to me. Get and wet though…not so much. Depends on how you pronounce get. It feels odd to pronouce it as “geht”, I’m more used to “git.” Huh.
Sort of. Hen and think have the same vowel sound to my ear.
I can progress from hen to then to theng to thing to think without consciously changing the vowel sound.
And here all along I’ve considered my accent to be a sort of generic, nondescript Midwestern-borne variety.
I’m gonna hafta thenk twice bout this theng.
It’s not a persnal thing, it’s a dialect thing. You often cannot hear very subtle differences in pronounciation unless they’re differences that your brain is trained to perceive.
Try learning a different language. You’ll find out REALLY quickly how many pronounciation differences you have trouble perceiving.
As to “ask,” I would point out that “aks” used to be how it was said, and anyway 95% of language snobs can’t pronounce “diphthong.”
Not only do I think I pronounce thing as theng, but my ears hear most other Americans say it that way too unless they’re, for example, a slack-jawed southerner or a New York wiseguy.
King, bring, sing, something, nothing, rink, link and trinket all have the same long e sound to my ear, as if I really am saying keeng, breeng and seeng.
I’m astonished that nobody else recognizes theng as the way to say that dang word.
Mine occasionally talks about the state of Wyome. Moms are weird.
Both pairs rhyme. (Anglophone Quebecker, grew up in Winnipeg).
On the other hand, “rider” and “writer” differ only in their initial vowel, not their middle consonant. 
Both pairs rhyme for me as well. Here’s how I say them. I’d be curious to hear them pronounced by people for whom they don’t rhyme.
Can you record yourself saying these words? Because I can’t even imagine anyone pronouncing them that way. Is there an example on YouTube? I don’t believe I have *ever *heard those words said with a long e. (Unless it was in some kind of weird exaggerated Mexican accent.)
To me both of the sets of words in the OP unquestionably rhyme, and it seems to me that they do in the “Neutral English” that seems to be standard on TV and other widesporead media. I agree with Eyebrows that I can’t imagine Homo lieralis’ weird “ee” pronunciation of “i”. It looks to me the way that the Frito Bandito and other now-politically-incorrect cartoon characters pronounced words, and to do that would make the speaker seem to have an exaggerated hispanic accent.
Here’s my own blind spot to throw into this duiscussion: I once a discussion (in print) about the way that “some people pronounce singer and finger the same way…” My reaction was “Arebn’t they pronounced the same way?” I was certainly raised to think so. But apparently it’s very common for people to bury the “g” in “singer” by nasalizing it, but to fully voice the one in “finger”, so they come out as sin’er and finger. * How do others feel about these two?
*and to all those who say “You probably don’t notice that you yourself pronounce “singer” and “finger” differently” – Nope. I’ve listened to me. I definitely pronounce them the same way, and see nothing odd about it.
Both pairs rhyme - mid-Atlantic with a touch of Pennsylvania Dutch (to this day I can’t say the word “route” without having a mental argument about the vowel sound).
I’m in the UK now and recently had a discussion with a friend who pointed out that in his accent “fear” and “year” don’t remotely rhyme (the latter being basically “yuh”).
It sounds like you have a stereotypical Mexican accent.