“You've been brainwashed.” is a fun little accusation to throw at people you disagree with. Because Christians often believe the same things as each other (because they read the same Bible) and because they often believe them passionately (or at least unapathetically) it's an insult that we're likely to receive at some time from someone. As my favourite TV psychology professor, Philip Zimbardo, says:
Those whose behavior violates our expectations about what is normal and appropriate are dismissed as kooks, weirdos, gullible, stupid, evil or masochistic deviants.
And the way we become such things is through brainwashing by our leaders.
In a way it's a compliment. While they are asserting that someone has manipulated you, they're also implying that you're not stupid enough to believe that stuff of your own accord—someone must have forced you to believe it. As Dictionary.com says it, brainwashing is:
Intensive, forcible indoctrination, usually political or religious, aimed at destroying a person's basic convictions and attitudes and replacing them with an alternative set of fixed beliefs. (From Chinese [Mandarin] xi nao: xi, to wash + nao, brain.)
Source: Dicitionary.com brainwashing
So the person who says you've been brainwashed is actually affirming your intelligence and attacking your leaders. The more horrifying situation, to them, would be that you've actually considered this nonsense and made a level-headed decision that it was correct. You've believed it willingly. But that's impossible. You're too clever for that. You must have been brainwashed.
So how do you go about answering someone who says you've been brainwashed?
First, I reckon you should think about whether they are right. Why do you believe what you believe? Is it just that your teachers are very persuasive and everyone else around you believes the same thing? Or have you decided for yourself, “Yes, this is true,” and been convinced from the Scriptures: rational, propositional, historical documents?
Secondly, ask the person why they think you've been brainwashed. Is it because they are shocked you could believe something so different to them? Is it because they think what you believe is stupid or doesn't make sense? Is it because of the strength of your convictions? Is it because lots of other people you know believe the same things?
Thirdly, explain to them why you believe what you believe. Show them how it makes sense even though it is different to what they believe. If you're game, throw it back to them: “Maybe you've been brainwashed too?” They are likely to be a product of their secular culture as much as you are a product of your Christian culture.
And fourthly, invite them along to your church meetings. Then they can see for themselves the way you are taught and you can have a better discussion about it.
Remember the classic verse on this topic that informs our attitude:
Have no fear of them, nor be troubled, but in your hearts regard Christ the Lord as holy, always being prepared to make a defense to anyone who asks you for a reason for the hope that is in you; yet do it with gentleness and respect, having a good conscience, so that, when you are slandered, those who revile your good behavior in Christ may be put to shame.
Source: 1 Peter 3:14–16
But what if you can't explain what you believe, at least not in a way that makes sense to someone else? That's ok, but it would be helpful for the “someone else” if you did spend some time thinking about the reasons you believe what you believe and thinking about how it all fits together.
Find other people to talk to about it, read lots—read our website! that's what it's here for. Most importantly read the Bible lots—the more you read the more you'll see how it all fits together and why it's worth trusting.