"4 How can you think of saying to your friend,* `Let me help you get rid of that speck in your eye,' when you can't see past the log in your own eye?"
a : at the farther side of : beyond
More: Past - Definition and More from the Free Merriam-Webster Dictionary
prep.More: past - definition of past by the Free Online Dictionary, Thesaurus and Encyclopedia.
2. Beyond in position; farther than: The house is a mile past the first stoplight. They walked past the memorial in silence.
- beyond in place or position ⇒ the library is past the church
More: Definition of past | Collins English Dictionary
To be honest with you, I couldn’t make head nor tail of the underlined part. In other words, I couldn't analyze it. Surfing the Net looking for "can't see past" and replied, "can't see past the end of nose." In a word, does the word past in the underlined part function as a preposition? Will you help me make it clear, please?
Google doesn't help much when it comes to language, does it? There are two idioms in your post. We can say "can't see past the end of his nose" of somebody who often fails to foresee likely consequences. This characteristic might signify a closed mind, or stupidity, or both. But that's not the idiom you are asking about.
A person who "can't see past" something is someone who, whenever that particular something looms, is suddenly unable to reason further or even perhaps to discuss things further. He is effectively blinded by the thing he can't see past.
Many if not all of us have fixed ideas or positions that prevent us from further reasoning or debate. Frequently, but not necessarily, these pertain to ideological or controversial matters, for example capital punishment, the legal status of recreational drugs, and abortion. A person who can't see past something may debate and advocate for his position, but will be incapable of hearing the arguments of others who disagree.