Liberal logic is an argument that has logical appeal to a liberal, but is nonsensical.
Logic is, by it's very nature, neutral,having neither liberal or conservative versions.
Let's build a list:
Translation: Let's make up a list of things that that we don't like and then claim that all liberals belive them.
an atheistic culture cannot harm anyone
Any form of culture an be either hamful or benign, no one with any grounding in reality disputes this. Moreover, liberalism and atheism are not one and the same and neither is required to accept the other, as the existence of liberal christians and conervative atheists proves.
but saying a prayer in class can cause tremendous harm
No one claims that prayer in class is harmful, nor is prayer forbidden in the classroom. The objection to classroom prayer, that you decietfully label as exclusive to liberalism, is to mandatory, teacher led, sectarian prayer in public schools which contains children of many diffrent religions and denominations, and children with no religious beliefs.
increasing spending by government must reduce poverty (no, dependency increases poverty)
That's not even a valid argument. There are far too many variables that you ignore in favour of making an ideological assumption that cannot be backed up with facts.
teaching abstinence must not reduce premarital sex
It doesn't. Period. All availible data shows that abstinence only sex ed. not only doesn't lead to a decrease i premarital sex, but also leads to an increase in teen pregnancies and STD infection.
widespread ownership of the largely defensive weapon of gun must not reduce crime
It dosen't reduce crime. In fact the vast majority of crimes couldnt be stopped just because the victim owns a gun. The vast majority of crimes happen when the victim i not even present.
that lack of government programs to rehabilitate criminals must not reduce crime
Imprisonment in and of itself does nothing to reduce crime.
that increasing taxes must increase government revenue
That's just simple mathematics. If you can't understand that you need to go back to pre-K.
(no, often people work less)
Taxation isn't limited to the income tax. There are a multitude of taxes that could be raised that would not be affected one bit by how much someone does or does not work.