You're misreading "sliver" as "silver" here. Some people have also translated these as "mote" and "beam".
The idea is something like that people are judging others with harsh standards that they can't apply to themselves, so they will notice or point out a very tiny problem related to another person, but not notice or point out a big problem related to themselves. It's a metaphor about having objects of different sizes stuck in one's eye and then a different activation threshold, so to speak, for acting on it depending on whose eye it is. This is akin to several kinds of cognitive bias.
The previous commenter mentioned that this saying appears in the Gospel of Thomas but it's much better known in this form from the Gospel of Matthew, which is considered canonical in Christianity.
The idea is something like that people are judging others with harsh standards that they can't apply to themselves, so they will notice or point out a very tiny problem related to another person, but not notice or point out a big problem related to themselves. It's a metaphor about having objects of different sizes stuck in one's eye and then a different activation threshold, so to speak, for acting on it depending on whose eye it is. This is akin to several kinds of cognitive bias.
https://en.wikipedia.org/wiki/Self-serving_bias
Edit: original context in Matthew:
https://en.wikipedia.org/wiki/The_Mote_and_the_Beam
The previous commenter mentioned that this saying appears in the Gospel of Thomas but it's much better known in this form from the Gospel of Matthew, which is considered canonical in Christianity.