Brief Answer:

And what do you think so many “variants” mean?

If you think it means we cannot reliably know what was originally written, then you are in opposition to the scholars who recognize we do have what was originally written, except for a small percentage of uncertainties, which are always plainly spelled out in the margins of the Bible.

Detailed Answer:

UNC Chapel Hill Professor Bart Ehrman has become one of the most popular scholars in his field, once he began writing about the variants (copy mistakes that vary from the original) in books such as Misquoting Jesus. This book has led many to think we cannot reconstruct what was originally written. He observed there are approximately 400,000 variants in the NT manuscript copies, and Ehrman even made a “top ten” mistakes list. My first thought when hearing this was, “This is significant, and Ehrman is a bright scholar”, however, first thoughts are not where you stop your thinking.

There are around 138,000 words in the entire NT, and with over 25,000 manuscript copies in Greek, Syriac, Latin and other languages, it becomes less surprising how many copy mistakes there are. The more manuscripts you have the more copy mistakes or variants you will have. If you only had 1 copy, then there would be zero variants, but how confident would you be that you have what was originally written? You couldn’t be, because with only one copy it would be easy for the copyist to purposefully or by accident make a mistake, and with nothing to compare against, we could never be sure it was accurate to the original.

In fact, how can Ehrman know what the top ten mistakes are unless he knew what was originally written? Do you see the problem? The way Ehrman’s popular books are written, many readers get the impression all those variants make us unable to reconstruct what was in the original writings, and these readers are often surprised to discover Ehrman’s writings and statements given toward other scholars, not the general public, demonstrate even Ehrman believes our Bible today is accurate to the original, despite the variants.

Even in an interview placed in the appendix of Misquoting Jesus on page 252, which has been removed in more recent editions of the book, this point is made clear:  

Interviewer: “Bruce Metzger, your mentor in textual criticism to whom this book is dedicated, has said that there is nothing in these variants of Scripture that challenges any essential Christian beliefs (e.g. the bodily resurrection of Jesus or the Trinity). Why do you believe these core tenets of Christian orthodoxy to be in jeopardy based on the scribal errors you discovered in the biblical manuscripts?” 

Ehrman: “Bruce Metzger is one of the great scholars of modern times, and I dedicated the book to him because he was both my inspiration for going into textual criticism and the person who trained me in the field. And even though we may disagree on important religious questions—he is a firmly committed Christian and I am not—we are in complete agreement on a number of very important historical and textual questions. If he and I were put in a room and asked to hammer out a consensus statement on what we think the original text of the NT probably looked like, there would be very few points of disagreement—maybe one or two dozen places out of many thousands.

The position I argue for in Misquoting Jesus does not actually stand at odds with Professor Metzger’s position that the essential Christian beliefs are not affected by textual variants in the manuscript tradition of the NT.” (Bart Ehrman, Misquoting Jesus, 252, emphasis added)

The variant readings almost always involve only issues of grammar, spelling, scribal slips of the pen, etc. And even if Metzger and Ehrman disagree on some places where the variants may impact the reading of a passage, core Christian beliefs are given over and over again throughout the Bible, so no core belief rests solely on an uncertain passage in the Bible. 

Another nice example, displaying someone in the general public assuming Ehrman teaches one thing and finding out he believes something entirely different, can be seen in a video found here, in which a Muslim expects Ehrman to claim the Trinity is not reliably found in the Bible because a disputed passage is involved. I think after reading Ehrman’s full quote on page 252 noted earlier, Ehrman does appear to be claiming this, but entirely refutes this idea in the video interview.