I am amazed at the degree of nonsense people will argue in defense of the indefensible.
Because it isn't indefensible that's why.
a) the notion that an entire race will be trained in using specific weapons, especially when described as a 'peaceful' race is absurd.
It isn't an entire race, it is the members of the adventuring class of that race, who spend a good deal of their time killing and pillaging... you know for goodness (but mostly for XP).
b) the notion that a race of people physically smaller than any other will collectively be able to inflict greater damage with specified weapons regardless of class or training is also absurd.
A slight bonus regardless of class. But a halfling wizard is still going to not be as good with a dagger as a fighter or rogue, so there you have the variance in ability.
As for a halfling being better at using daggers generally than a human wizard, no it doesn't bother me. In medieval societies having the entire adult male population being trained in the use of a particular weapon was not uncommon. At its most extreme it was mandatory. In 1252 for example the 'Assize of Arms' ensured that all Englishmen were ordered, by law, that every man between the age of 15 to 60 years old should equip themselves with a bow and arrows. The Plantagenet King Edward III took this further and decreed the Archery Law in 1363 which commanded the obligatory practice of archery on Sundays and holidays.
So in a world when your village might be attacked by a random encounter at any moment, it only make sense that the entire class of
adventuring halflings (mostly dextrous, mostly male, mostly young) would have training in the sword and sling. Those trained men would also come in handy when the human king wants a levy of slingers from your villages to fulfill your feudal obligations as well.
C) the knock on effects of including such racial abilities leads to other absurd rulings in the name of 'game balance'.
We've explained over and over why it isn't unreasonable, and why it hasn't been unreasonable since halflings first showed up in the game to have a bonus to attack and/or damage with their favoured weapons. Heck, even Tolkien mentions in his prologue to the Lord of the Rings concerning hobbits, that hobbits are adept with slings and throwing stones, which is where this whole bonus comes from. The grand old professor understood that a particular people or region can have a martial culture based around a particular weapon.