Why did Mohammed suggest that breaking oaths was okay?

Mohammad meant that he [and the Muslims] were not bound by any oaths.

Refer to Surat at Tauba, 9th Chapter of the Qur'an which is all about Mohammad breaking his oath in the Treaty of Hudaibiyya.

Any fool who trusts a Muslim, deserves to suffer for that folly.

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The meaning seems pretty clear to me. The quote doesn't seem very genuine though as the language is too modern for the Quran. What does it matter what Mohammed meant? His beliefs and sayings are no more relevant than Hitler's were.

i dont know what HE said, but i do understand if an oath is false, or evil, it must be considered sin, to be repented of and forsaken

Muhammad was a depraved, vile, murdering, raping, warlord and pedophile. He lied about his visions of Allah, he lied about everything else, all to satisfy his narcissism, craving for power, and sickening sexual desires. It surprised you that he was a hypocrite?

muhammad was a very confused human so who knows what he meant, but it should not surprise us in the least for him going the direct opposite of what God says, since he was anti-christ in his religion.

because islam is a religion created to hold a country together during crisis, and there is proof

Because he is a liar and would lie and cheat if it enhance his agenda.

The Gospel ended with Jesus.

I think the short answer is that he is not to be trusted.