Channy, you have just been given, in the comment immediately above your own, the four correct declensions for number of the noun "läkare". The word "läkarer" is among them.
So that is "why not 'läkarer'." What more do you need to know?
Since 1999, the Swedish Academy has identifies seven different way of forming the plural of Swedish nouns. But for any given noun, only one of the seven is correct. You can't just choose any plural you like.
There are in fact Swedish nouns that form their plural by adding -er. That is the so-called Third Declension. Examples include fest/fester, restaurang/restauranger, kafé/kaféer, and månad/månader.
But läkare is not one of the Third Declension nouns. It is a Sixth Declension noun: läkare/läkare (no change).
I googled a bit and found out that the Swedish word for heal, "läka", is very close to some Slavic words for farmacy, right?
Maybe they have a common background. Unfortunately I don't understand what is said in Svensk etymologisk ordbok because of all the abbreviations :). Hopefully someone else does.
I found something as well. My presumption was wrong. It's the other way around. The Slavic languages borrowed the word from Gothic. See here under Bulgarian in Etymology 2: http://en.wiktionary.org/wiki/%D0%BB%D0%B5%D0%BA#Bulgarian
Here we go! Plural of nouns endning in -er:
Some, but very few, nouns that end in a consonant, belong to the first declension (-or plural). Among them
åder - ådror (vein - veins)
Many nouns with unstressed ending in -er belong to the second declension (-ar plural), e.g.
förälder - föräldrar (parent - parents)
syster - systrar (sister - sisters)
vinter - vintrar (winter - winters)
There are also foreign words ending in -er in this group, e.g.
jumper - jumprar
reporter - reportrar
Many multisyllabe nouns with a final stress belong to the third declension (-er plural), e.g.
kavaljer - kavaljerer (cavalier - cavaliers)
officer - officerare (officer - officers)
Some nouns ending in -er that denote people and professions belong to the fifth declension (zero plural), e.g.
elektiker - elektriker (electrician - electricians)
indier - indier (Indian -Indians)
That was a very good point! The Swedish plural is really complicated. I will try to find some info about this. If you compare "musiker" and "förälder", one difference is that the first syllable is stressed in musiker and the second one is stressed in förälder. Anyway, we need a new rule here! I'll be back...
As a Dane I hear "my parents are delicious" because läkare sounds like lækre in Danish the way it's being pronounced here XD Another example of words that sound alike, but definitely don't mean the same between our closely related languages.
I think delicious/lækre in this context to me is like the swedish 'vacker' I chuckled when I heard it :b
Haha well, I'll be dammed, doesn't surprise me so much though :D
Love learning Swedish and looking forward to put it to practice in January of next year!
I Probably have it easier than most non Scandinavians though ;b
Thanks for being such a contributing member of this community! Have all the lingots ^^