There is no way to know the truth
Is this true? Because if so it is a contradiction.
There are ways to know certain things aren't true
This is just another way of making a truth claim even though you can't know the truth.
...you should always seek it
How do you go about seeking the correct one if striving for truth is valuable?
Who says seeking truth is something we ought to do? Particularly if knowing the truth is an impossibility. These are all assertions as to what we should do without any justification as to why we should do them.
I'm being slightly annoying to shine your own standards on yourself. Not meant to be combative.