Why do governments pick such odd numbers for metal content in coins?

It started long before that though, in Europe. The standard weight used for precious metals was the marc (about 8 oz.). It is a unit of measurement that had been used for centuries. Not really sure where or when it originated, but it certainly goes back to the time of Charlemagne and probably long before.

The problem was, every city had its own definition of a marc. And when they minted coins, gold or silver, the decree would be that X amount of coins of a given denomination would be struck per each mark of silver or gold. For the Spanish, it was 68 reales per marc. Their marc was the marco Castellano, or 230.0465 grams of pure silver. Of course they did not mint the coins in pure silver, but used varying degrees of fineness over the years, as did all nations. But that's another story.

As I said, other cities used varying units of weight. For example - the defintions of a pound or 16 oz. -

Cologne = 2 marc = 467.620 grams
French = 2 marc = 489.506
Aachen = 32 loth = 467.040
Amsterdam troy = 2 mark = 492.168
Antwerp = 2 mark = 468.800
Hamburg = 512 pennyweight = 484.690
Lisbon = 2 marcas = 459.100
Lucerne = medical pound = 357.950
Munich = 560.000
Naples = 12 ounces = 320.759
Stockholm = 425.34

This was really the start, and the reason for, currency exchanges. But back then they called them money changers as they had since biblical times. The various currencies of nations were all worth different amounts depending on where you were at the time.

By the time large silver deposits were first discovered in Germany, mid 1500's, the Cologne marc was settled upon as the standard for weight and it was used until the 1800's. All other nations measures of weight was measured against the Cologne marc and value for currency exchange was based upon it.

Now that's probably a lot more than you wanted to know, but it is the explanation for the answer to your question as to how they decided upon what seems to you to be such strange numbers for the weights of coins. But back then, they were not strange or uneven numbers. They were nice round numbers.