Linking Words : Contrasting

One of the function using linking words is to contrasting ideas between yours and the other party.

But and However

Their main function is to say the opposite opinion, but there slightly different usage between them.

But : can only be used in the middle of the sentence.
However : can be used in the beginning of the sentence

I wish you were here, but you are not.
I wish you were here. However, you are not.

See? :)

On the other hand

Is used to contrast the ideas. It also can be used in the midlle of the sentence.

I like fish as main course, on the other hand my father prefers beef

While and Whereas

Both are usually used between two complete phrases/clauses

I have to go to school every morning, while my sister goes to the office.
I know that having a car is not the only parameter of rich, whereas my brother think it is a must have.

Even if both of them are used to contrast the idea, whereas is stronger than while.

Despite an In Spite Of

Both are followed by noun or gerund.

I can do the test despite being too lazy since last week
She cannot do the test in spite of having read all the materials.

Despite The Fact That and In Spite Of The Fact That

Despite and In Spite Of can be followed by a phrase/clause (subject + verb +...) by adding
"the fact that"...

She cannot do the test in spite of the fact that she has read all the materials
I can do the test despite the fact that i have been too lazy since last week.

Although and Eventhough

Their meaning is similar. Nothing different.
Both are used to contrast the ideas followed by clause (subject + verb + ...)

Lolo said the painting was amazing although it was hard to understand
Jaron said Kay was sheathed in gorgeous dress eventhough she didn't like it