I'm reading Deuteronomy now and Moses proclaims a lot of things to the Israelites in the initial chapters. It's one long speech. It seems the things he said were instructed by God. See this verse:

Deuteronomy 1:3;

In the fortieth year, on the first day of the eleventh month, Moses proclaimed to the Israelites all that the Lord had commanded him concerning them.

Moses gives a recap of the things that had happened in the previous 40 years and he also instructs the Israelites a lot of things like living God and keeping his commandments. The thing regarding oaths caught my eye.

Fear the Lord your God, serve him only and take your oaths in his name. Deuteronomy 6:13 NIV

Also this.

Fear the Lord your God and serve him. Hold fast to him and take your oaths in his name. Deuteronomy 10:20 NIV

The instructions surprised me because Jesus tells us not to take oaths and that we should simply say yes or no.

“Again, you have heard that it was said to the people long ago, ‘Do not break your oath, but fulfill to the Lord the vows you have made.’ But I tell you, do not swear an oath at all: either by heaven, for it is God’s throne; or by the earth, for it is his footstool; or by Jerusalem, for it is the city of the Great King. All you need to say is simply ‘Yes’ or ‘No’; anything beyond this comes from the evil one. Matthew 5:33‭-‬35‭, ‬37 NIV

God urges the people to do one thing and later the polar opposite thing. Surely, there must be something that I've missed. I think there was a silly opinion among people that is okay to break oaths made on the temple gate but it's not okay to break oaths made on the temple coins. Jesus calls out the silliness of that. So is this related to that in a way or the Deuteronomy one needs to be viewed in some context?

In Deuteronomy Moses teaches to make oaths in the Lord's name:

Fear the Lord your God, serve him only and take your oaths in his name. 
Deuteronomy 6:13 NIV

Fear the Lord your God and serve him. Hold fast to him and take your oaths in his name. 
Deuteronomy 10:20 NIV

The instructions surprised me because Jesus to take oaths at all and that we should simply say yes or no.

“Again, you have heard that it was said to the people long ago, ‘Do not break your oath, but fulfill to the Lord the vows you have made.’ But I tell you, do not swear an oath at all: either by heaven, for it is God’s throne; or by the earth, for it is his footstool; or by Jerusalem, for it is the city of the Great King. All you need to say is simply ‘Yes’ or ‘No’; anything beyond this comes from the evil one. 
Matthew 5:33‭-‬35‭, ‬37 NIV

God urges the people to do one thing and later the polar opposite thing. Surely, there must be something that I've missed. 

I recall learning that there was a silly opinion among people that it was okay to break oaths made on the temple gate but it's not okay to break oaths made on the temple coins. Jesus calls out the silliness of that. So is this related to that in a way or the Deuteronomy one needs to be viewed in some context?

How have various theologians resolved this contradiction?