While I can't exactly give much of an answer in the way of why they currently continue exist, I can tell you that it became a country in the first place because of religious differences rather than linguistic.

Belgium became independent from the Netherlands in a revolution in 1830, sparked largely by dissatisfaction with William I's supposedly despotic rule, but motivated by the fact that the majority of people in the southern provinces that would become Belgium were Roman Catholic, while those of the north were Dutch Reformed Protestants. The revolution went largely unchallenged by the Dutch army, which pulled out of the provinces after the defection of most of their forces from the south.

Belgium was officially recognised quite early on as well, as William I appealed to the Great Powers of Europe to help him put an end to the revolution after the Belgian Congress officially voted to secede. Instead of helping him, however, the Great Powers chose to recognise Belgium's independence, which must have been a powerful boon to the already fervent nationalistic ideals within the country.

The Dutch did invade, however, a year into Belgium's independence after they installed Leopold I as their king; the campaign was short and ultimately failed thanks to French military intervention, and in the end the Dutch officially recognised Belgium's independence in 1839.

To give a sort of TLDR; the Belgians became independent because religious differences and dissatisfaction with Dutch rule sparked revolution; Belgian nationalism became a thing; it was strengthened by recognition from the Great Powers; and ratified by the French military.

It's possible that the reason Belgium continues to exist despite their completely split population is because of this fought-for independence; even though the majority speak Dutch (something like 60%) it's possible that the reminder of Belgium having gained independence from the Dutch in the 1830s reinforces the idea that rejoining the Netherlands isn't the best idea.

Sources:

• Fishman, J. S. (1971), 'The London Conference of 1830', Tijdschrift voor Geschiedenis, 84:3, pp.418-28
• Schroeder, P. (1994), The Transformation of European Politics, 1763 - 1848
• Witte, E., et al. (2009), Political History of Belgium: From 1830 Onwards

EDIT: defection, not detection.

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