"Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect," 1 Peter 3:15
When sharing your faith, the person listening to you does not have to agree with you or even receive your message. You are not validated by their response. You are simply sharing what you know. Frustration or anger at rejection is an indication that you might not be so sure about your faith yourself. Be clear about what you believe and why.
What IS mandatory is to make your position clear, logical and internally consistent. I might be wrong but at the very least I try to be consistent. This means you don't bother trying to build a detailed, academic argument if you are not academically trained. Be a witness. Tell what you know, not what some clever person told you.
Don't claim to be an authority, you are setting yourself up for a fall. Even if you ARE an authority it is a mistake. Show some humility. You are sharing your faith with another. It is not necessary to build an airtight legal case. In the "Scopes Monkey Trial" of 1925, William Jennings-Bryan claimed to be a Biblical authority. He was not, and lawyer Clarence Darrow made a monkey out of him over national radio.
Be honest about who you are, what you know and what you don't know. Hypocrisy is the unpardonable sin as far as unbelievers are concerned.
“Marx is to communism what Christianity was to the Rulers of the Holy Roman Empire; convenient as a banner, irrelevant as a guide.”
Richard M. Nixon--The Real War