What developments in modern science cause people to doubt God’s existence and his promise for man’s everlasting life?

First, we should observe that many (probably most) people reconcile their religious faith with their understanding of science. They do not see the two as mutually exclusive. But science does tend to cast doubt on literal interpretations of religious texts, most of which were written in a pre-scientific era. The most famous example of this, perhaps, is the scientific theory of evolution by natural selection. This contradicts a literal reading of most creation stories, such as that written in the Biblical book of Genesis, in which God created the earth and its living things in seven days. Likewise, the Copernican model of the universe contradicts the Bible, which describes the sun as being in motion. This is why Copernicus's book was banned by the Church after his death. As for the issue of everlasting life, science can really take no position on that. Science is concerned with testable theories, and scientists simply cannot test a theory about life after death. So since the sixteenth century, modern science has reached observable, testable conclusions that contradict some things in religious texts. But because the core claims of the major religions are supernatural by definition, they cannot be tested by science and thus cannot be proven nor disproven. They are matters of personal faith, which is the antithesis of the critical approach fundamental to science.
https://plato.stanford.edu/entries/religion-science/