1. The Gospels give contradictory accounts of Jesus life, death, and resurrection.
Ask any detective or journalist and they will tell you that eyewitness accounts of the same event are never exactly alike. We have an overwhelming amount of redundancy between the four Gospels, more overlap than dissimilarity. When there are differences, they are minor and do not significantly change the basic account. If anything, it would be more suspicious if everyone told exactly the same details, as if they had collaborated beforehand to get their story straight.
2. Paul and Jesus teach different things.
People argue that since the Gospels are full of Jesus teachings on the kingdom of God while Paul's focus seems to be on justification, Paul must be teaching something Jesus never taught nor intended to teach. However, this reasoning misunderstand how revelation in the Bible unfolds. Revelation unfolds in an organic step-by-step way, rather than all at once. Christ inaugurated what the apostles built upon through the inspiration of the Holy Spirit. Additionally, a concept may be present despite the lack of specific vocabulary naming the concept. Christ clearly indicated that salvation could only come through him (Jn. 3:16-17; Jn. 14:6) despite never using the word justification. Likewise, Paul also taught that Christians who trust in Christ have an eternal inheritance, are called sons of God, and will be resurrected when Christ returns. All these things are elements of the kingdom Christ also taught.
3. James and Paul teach two different salvations.
Throughout his epistles, Paul emphasizes over and over again justification by faith alone. This is especially clear in Romans and Galatians. The book of James would seem to teach a contradictory salvation of faith plus works (Jm. 2:14-17). However, the book of James never denies faith is necessary for salvation. Its focus on works is to show that live faith, like a live tree, blossoms and bears fruit. Faith that is dead does not bear good fruit and so proves itself to be worthless. This is not denying justification by faith but simply showing that justification and sanctification are connected, albeit in a strict order. Justification always comes first as an act of God while sanctification comes afterward as an ongoing work of God.
4. Christianity is a primitive religion that the apostles made up to fit the needs of the community.
The argument goes that Christianity is no longer suited to the modern world, that the apostles supposedly edited, adapted, and transformed Jesus to fit the needs of their community. However, this is very unlikely. The apostles wrote their Gospels not long after Jesus ascended and at a time when there were still many people alive who had known Jesus, been healed by Jesus, and heard Jesus teachings. Luke mentions Cleopas (Lk. 24) as someone who can confirm that Luke was reporting truthfully. If anyone had doubts that the apostles were changing Jesus teachings, they could have gone to plenty of people and compared the two. It is highly unlikely the apostles would have changed Jesus theology while there were still people who could say they were lying.
5. The Bible must have errors because of all the variants among the manuscripts.
The similarities between the core teachings of the New Testament manuscripts far outweigh the dissimilarities. Additionally, the differences are so minor that they do not change the meaning of the theology in any significant ways. This is remarkable given the fact that manuscripts were tediously copied by hand. For instance, many of the variations are copying mistakes that leave out a word like and or but or mix up the order of two words like Jesus Christ copied to Christ Jesus.
6. It is impossible to know what the original biblical manuscripts taught.
The truth is, we can actually know with very high probability what the original biblical manuscripts said because we have so many copies, massive amounts compared to other literature of the time. We only have one copy of the most popular comic playwright of the Ancient World compared to over 6,000 New Testament manuscripts, all of which say pretty much the same thing.