It's wrong, but it is quite a good mistake I thought!

Exactly my point grumppa! I'm glad at least someone has 'got' my OP

To return to the OP, this is an interesting case of an error being as meaningful as what was intended. Depreciate used transitively means to reduce the value of something, so someone who self-depreciates is talking him/herself down; very similar to self-deprecating.

But I am straying into Pedants' Corner.....

Muphry's law strikes again!

Muphry's law is an adage that states: "If you write anything criticizing editing or proofreading, there will be a fault of some kind in what you have written." The name is a deliberate misspelling of Murphy's law.

I am very bad at seeing these and my typing is not accurate. I tend to read and hear the words and recognise the sound rather than the pattern of letters.
Proof reading anything I have written is really difficult.

DH was convinced it was "one fowl swoop" and not "fell swoop". He had used the former all his life without realising it was incorrect.

Oh and ' tow the line' not toe and ' state of the ark'

I loved the ' while and wipe' one. I wanted to write something about Cynthia Payne.

I have just caught up with this, and I have had a good laugh, thank you Anna and nina, that will teach me not to make fun of a very dear friend. (I almost typed Fiend, there!).

Or even referred and not refereed

Anna: you beat me to it

It's no good - I'm sure you meant to type Customs and Excise, PRINTMISS

Ooh...!!!

My friend who was very good at book-keeping and accounts, always refereed to the Customs and Exercise, instead of Custom and Exise

Why did I just know I'd get it as soon as I clicked on 'post message'?...

If I had read (as opposed to heard) "self-depreciating" in the context given in the OP, I would have simply assumed that it was a typo. I don't know about anyone else, but my fingers often add superfluous letters when I'm typing, and such errors are very easy to overlook when doing a quick spell-check.

I was amused when somebody recently announced that her furry had been aroused but was much too tactful to point this out. Similarly referring to what I assume was meant to be a trug as a trough, but maybe again, the couple in question might have been very very strong and able to carry a trough around with them.
Charitably, one should blame iPad/iPhone predictive spelling.
I heard today of a friend of a friend who emailed an art dealer recently to get an estimate for 2 canal paintings she wished to sell. She got a very polite reply suggesting she might like to start the word in question with the "missing C" the next time she wrote.

Nana, thought it was 'jampit!

My DS makes his own words up all the time, or think he's got it right when he really hasn't and he just makes me laugh.

It's when it should be its and vice versa...

Of when it should be have. Grrrr!

expresso

I have a few:
Expression instead of espresso;
Escape goat, instead of a scapegoat;
Mute point;
damp squid;
Baited breath;
And here in Scotland, 'he jamp off', instead of jumped.

Can't remember where I first came across this one, but I've seen it a few times lately - defiantly instead of definitely. It can prove to be quite amusing!

Dessimation instead of decimation was another, and Rddie for Eddie...apologies for being so picky. The whip for wipe was a shocker - I wasn't sure what to expect: kinkiness or issues? I know why these mistakes happen but they irritate the heck out of me...