Self refuting statements are as common as fruit flies in any religious or political debate, and in many cases are just as annoying. One example is "that's just your opinion". This argument is useless, because it adds nothing to the discussion. It is lazy, because it can be used against literally any statement, no matter how reasonable. It is self refuting, because "that's just your opinion" is, of course, just an opinion, usually in defence of another opinion.
An unfortunate feature of debate is that all statements of truth proceed from a mind. In other words, they are all opinions. An opinion is a belief or judgement on a given topic of discussion. By this fairly standard definition, even 1 + 1 = 2 is an opinion. It just happens to be a true opinion that can only be dismissed by a complete and total numpty.
There are two kinds of opinions in the world. Subjective and objective. A subjective opinion is an opinion which changes in truth value according to the one expressing it. "Lemon ice cream is the best ice cream" is a subjective opinion. I personally love lemon ice cream, not just for the flavor, but also for the nostalgic value. It brings back childhood memories. But another person might not even like the taste. Neither opinion is correct, and thus it is not even worth arguing about it.
Objective opinions are opinions about the reality that ultimately exists outside of the human mind. Some opinions can be more correct than others. For example, "the world is flat" is an opinion. It is, however, a wrong opinion. Now, a flat earther might say to me "but that's just your opinion". Yes, it is, but it is the correct opinion. Saying "that's just your opinion" does not make the world flat, neither does it open the possibility that the world is flat. "That's just your opinion" is a poor defence for a poor worldview.
"The Bible is the infallible, inerrant word of the Living God" is an objective opinion. If it is true, it is true, and it does not matter how much one may reject it. Similarly, if it is false, it is false, and no amount of belief will change that. "That's just your opinion" will never be a valid argument for or against it. The correct statement, if you insist on bringing the word "opinion" into this, is "defend your opinion". "The world is flat." "Ok, defend that opinion." Great, now we can have a reasonable discussion about the shape of the earth. "The Bible is the inerrant, infallible word of the Living God." "Ok, defend that opinion." Great, now we can have a reasonable discussion.
Of course, defending the Bible depends on the existing opinions of the one you are defending it against. The cosmological argument might work on an atheist, it won't even graze a Muslim, because Muslims are already Theists. The Islamic dilemma is devastating to a Muslim, a Mormon won't blink twice, because they don't believe the Qur'an. Joseph Smith's failed prophecies demolish Mormonism even by its own standards, but what Jehovah's Witness will repent and turn to Christ because Joseph Smith lied? He's not their prophet. The list goes on. The case for Christianity must be tailored to individual unbelievers. But no matter what the unbeliever believes, "that's just your opinion" will never change the fact that Christ is risen.
And He is indeed risen. For every lie you've ever told, He died. For every wrong opinion you have ever expressed, He was crucified. Your sins lead to His death, but by God's power, He rose again. If this is an opinion you share, it is His opinion that you should receive eternal life. Repent of your sin, believe in the risen Lord, and you will receive an inheritance you cannot even comprehend right now.