I have learnt that weshalb is a question and deshalb a statement but watching a video from a usually reliable German teacher on YouTube I came across this example in a B2 level "Brief schreiben":
Leider ließ diese Reise zu wünschen übrig und entsprach keinefalls der Beschreibung, weshalb ich dieser Beschwerdung verfasst habe.
Wouldn't deshalb be better in this instance? And, as there is no question raised, is weshalb being used correctly?
"weshalb ich dieser Beschwerdung verfasst habe" is a type of relative clause, and some German relative pronouns are homonymous with interrogative pronouns. This is similar to the same phenomenon in English:
We banned the player who cheated at bidding.
"the player who cheated" is a similar type of relative construction, and it uses the same pronoun who as the simple question "Who cheated?".
One important thing you mentioned is that these types of clauses do not constitute questions. The question word at the head of these clauses has the function of determining what they talk about. In the given example, the clause introduced by weshalb talks about a reason. In fact, the example could easily be reworded.
Die Reise lies zu wünschen übrig, weshalb ich diese Beschwerde verfasst habe.
Die Reise lies zu wünschen übrig. Deshalb habe ich diese Beschwerde verfasst.
As the paraphrase indicates, deshalb (and similarly weshalb) refers to the content of the preceding sentence: the trip having been unsatisfying is the reason for writing the complaint.
It also becomes clear that this type of subordinate clause introduced by a question word is different from ordinary relative clauses in that the latter refer to some element of the preceding sentence, but not the sentence as a whole. In German grammar, they are known as weiterführende Relativsätze.
Some further examples:
Bei dem Film habe ich Rotz und Wasser geheult, was mir sonst nie passiert.
Watching that movie I was crying my eyes out, which never happens to me.
Wir sind dann doch noch pünktlich angekommen, womit ich gar nicht mehr gerechnet hatte.
We did arrive on time after all, which I hadn't expected.
Note that question words can also introduce regular relative clauses, i.e. those referring back to a noun or pronoun.
Das ist etwas, was mir sonst nie passiert.
That's something that never happens to me.Es gab einiges, womit ich nicht gerechnet habe.
There were some things I didn't expect.
It has to be 'weshalb' as it initiates a subordinate, a relative clause:
Leider ließ die Reise zu wünschen übrig, weshalb ich eine Beschwerde verfasst habe.
The use of 'deshalb' would be wrong and can only be used with main clauses:
Leider ließ die Reise zu wünschen übrig, und ich habe deshalb eine Beschwerde verfasst.
As the other answers already explained, it's a relative clause.
I'd just like to add that English seems to have a similar construction (somewhat archaic/legalese) using "wherefore":
Example from some EU regulation about olive oil:
English: It is necessary to ensure a harmonious continuation of income support payments to olive producers, wherefore the option of postponing the introduction of the single payment scheme should not apply.
Deutsch: Es muss für eine harmonische Fortsetzung der Einkommensstützungszahlungen an die Olivenerzeuger gesorgt werden, weshalb von der Möglichkeit, die Einführung der Betriebsprämienregelung zu verschieben, kein Gebrauch gemacht werden sollte.
Source: https://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=COM:2003:0698:FIN:EN:PDF (page 14) via Linguee.
