What is the political goal for an independent country to deny a common language with a bigger neighbour?

Question

I do not see the point in claiming there are separate languages named "Montenegrian", "Moldavian" or "Macedonian" when those were actually made up during the communism era and didn't exist before the Second World War. Before the First World War, Serbian was the official language of the Kingdom of Montenegro. People living in contemporary Macedonia used to identify themselves as Bulgarians, and Romanian speaking people in Russian Empire (today part of Moldavia and Ukraine) also identified themselves as Romanians.

I understand such countries need to develop their identity after more than 40 years of communism. However I do not see how it would help those isolated, small and poor countries to develop to deny their common language with their larger neighbor. Having a common language with a larger, more widely recognized country would only help to get foreign people interested in the region.

Also, I do not see why former Yugoslav countries now deny the existence of a common Serbo-Croatian language, although this makes slightly more sense than the above, considering the atrocious crimes each of those communities committed against each other during the 1990s, and the fact that the writing can be either in Cyrillic or in Latin characters.

In French speaking Switzerland or Belgium we have no problem saying we speak French, this do not create any problems - we don't have to claim we speak "Swiss" or "Belgian" - and that despite the fact a small fraction of our languages actually differs (the #1 difference is how we count).

Answer 1

"Why do they deny it?" — the answer is, they do not deny.

Moldova

Moldovan President Nicolae Timofti called for making Romanian Moldova's official language rather than Moldovan, as currently specified in the constitution.

"We are ethnic Romanians, although we call ourselves Moldovans," the president said in a speech at Moldova's Academy of Sciences marking National Language Day on August 31 in Chisinau.

"Let us learn and accept this fact once and for all and concentrate on other problems," he said.

— Radio Liberty

Update 2017-12-14:

The Government supports the legislative initiative to amend Article 13 of the Constitution of Moldova by replacing the phrase "Moldovan language, functioning on the basis of the Latin script" with "Romanian language", the government's communication and protocol department has reported. — Moldpres

Montenegro

Indeed, there exists a certain amount of controversy in Montenegro as per how to call the official language of the country. This article sums it up very well, and the most common argument is:

"The official language in Montenegro is Montenegrin, but it may be referred to as Serbian, Bosnian or Croatian" — Miodrag Vukovic, a representative of the ruling DPS

Being a member of Linguistics.SE community who is especially interested in dialectology, the OP knows very well that the dialects of language always vary. Even the languages spoken by people from the same family may differ by a certain extent. Of course, this difference is very small but still noticeable. Increasing the scope to a street, village, region etc. makes the differences more evident. So we can safely assume that variations of Serbian language, spoken in Beograd and Crna Gora are essentially different to qualify for being essentially different dialects.

Naturally, Montenegrins may prefer having linguistic standards established by their own linguistic institutes, avoiding any dependence on Serbian Language Institute that seems to be responsible for establishing the rules for Standard Serbian.
To better understand the alternative, imagine if Montenegrin and Serbian scientists would publish books "The Grammar of Standard Serbian", contradicting to each other the same way as the respective dialects differ. There would be no problem at all if one of these books were called "Standard Montenegrin".