Why did president wilson feel like his fourteen points would create lasting peace ?

That is because Woodraw Wilson,the US president thought that the 14 points can tackle causes that lead to war.
Here are a few examples:

The alliance system- Alliance system was one of the reason that caused the outburst of World War One(WWI),because the nations would drag one another into the war once attacked as signed to the alliance system.

There was a point that secret diplomacy is not allowed to tackle the problem.

Militarism- Armament race had intensified the nation's will to wage a war with their armies and weapons,fighting for national glory as well as defending themselves.

There are solutions in the 14 points as well,such as the reduction of armaments.

Imperialism- Theses nations were the most likely to wage war for national glory and act irrariinal thus have to be tackled.

Points such as Freedom of the seas in peace and war,removal of international trade barriers were aimed towards the issue.

However,as much as he believed that it could create peace,many weren't practical as they cannot be executed easily among countries,given the interests in conflict.

Hope it helps!