Reading the scripture in context is essential to understanding meaning. Consider the contradictory example of "all things being possible for God" yet "God cannot sin." If there are things that God cannot do, then why do people say all things are possible for God?
The concept that "all things are possible for God" comes in part from Matthew 19:26 NRSV "For mortals it is impossible, but for God all things are possible." (also in Mark 10:27; Luke 18:27) In the context of this verse, Jesus is speaking of a very particular subject: salvation.
In context, Jesus has just told the parable of the rich man, saying that it is difficult for a rich man to be saved due to his love of worldly possessions. Jesus says that it is easier for a camel to go through the eye of sewing needle. In response, the disciples exclaim, "Then who can be saved?" (Matthew 19:25 NRSV; Luke 18:26; Mark 10:26)
It is virtually impossible for a camel
to go through the eye of a needle, which is why the disciples are so
upset. Jesus then confirms their fear in his response, but then gives
them hope: "For mortals it is impossible, but for God all things
are possible." (Matthew 19:26 NRSV; Mark 10:27; Luke 18:27)
Similar statements are also made in these verses:
In Luke 1:37, the context is that the virgin birth is possible for God.
In Jeremiah 32:27, the context is redemption.
In Genesis 1, the context is the very creation of the universe.
The Bible is very clear that there are many things that God cannot do. "It is impossible for God to lie," (Hebrews 6:18 NRSV) and, in general, God cannot sin because he is holy (1 Peter 1:16; Leviticus 19:2).
It is also impossible for God to change. God plainly states, "I the LORD do not change." (Malachi 3:6 NRSV) and James says, "...the Father of the heavenly lights, who does not change like shifting shadows." (James 1:17 NRSV)
It is impossible for God to be tired. Isaiah says, "Do you not know? Have you not heard? The LORD is the everlasting God, the Creator of the ends of the earth. He will not grow tired or weary, and his understanding no one can fathom." (Isaiah 40:28 NRSV)
It is impossible for God to tempt us with evil. James bluntly says, "No one, when tempted, should say, 'I am being tempted by God'; for God cannot be tempted by evil and he himself tempts no one. But one is tempted by one's own desire, being lured and enticed by it..." (James 1:13-14 NRSV)
All things are possible for God, except that which opposes his very nature. God can't sin, he can't lie, he can't change, he can't get tired, God can't tempt us or be tempted by evil, and God can't be anything except perfect/holy.
Therefore, scriptures that claim that everything is possible for God tend to come with the assumption that everything is possible as long as it does not oppose God's nature and character. If God created the entire universe, then certainly anything else is possible for him.
Likewise, verses that claim "I can do all things through [Jesus Christ] who strengthens me," (Philippians 4:13 NRSV) also need to be read in context to understand what the author is saying. In this particular verse, Paul is referring to the secret of "being well-fed and of going hungry, of having plenty and of being in need." (Philippians 4:12 NRSV)
Specific Questions non-believers ask:
Can God sin? No.
Can God make a stone too big for him to lift? No. Such a creation would contradict God's nature. Some would suggest that this truth contradicts God's all-powerful nature, but the true God does have limitations, like not being able to sin or get tired, yet he can create the entire universe in all its complexity and then circumvent his creation to allow a virgin birth.