This picture was taken from a private Facebook Group named, Sola Scriptura: A Foundation of Sand. The Roman Catholic who posted it said Luther admitted and sought to justify "his lack of sexual restraint and sin" and that "Luther was a prideful mentally-emotionally disturbed apostate."
While this quote has been covered here in-depth before, it appears to be popular on social media with people unable to approach history with integrity or lack the simple desire (or ability!) to do a basic web-search.
Here is a simple method of response.
1. The documentation is partly erroneous. The quote is said to be on page 33 of Martin Luthers Werke, kritische Gesamtausgabe, vol. 2. It is not. It's on page 107 of WA TR 2. Also, ask anyone using this documentation who the English translator was or where the English translation presented in this picture actually comes from. The English translation being utilized is not from Luther's Works, American Edition, Volume 54, p. 154.
2. This is not something Luther is known to have actually written. It is from a collection of secondhand comments written down by Luther's friends and students, published after his death, known in English as The Table Talk.
3. There are multiple versions of Table Talk statements varying in reliability. That reliability is determined, in part, on how many people recorded the statement. This particular statement was recorded by only one person (a person little is known about). The extant manuscript version is a handwritten copy made sometime between 1551 and 1557 of the missing original. Keep in mind, the original statement is alleged to have been uttered between 1531-1532.
4. This particular Table Talk utterance was not available for roughly 350 years until it was published in 1888. It contains textual anomalies in which what was written originally must be conjectured. In the Weimar edition of Luther's writings, a footnote is included noting the text is unclear and is a probable reading.
5. If the statement is a rendering of what Luther said, there is no context for the remark. There is no meaningful historical or textual context to determine what Luther meant: Was he jesting? Was he summarizing someone else's argument? Was he using hyperbole? Was he making a point to correspond to some aspect of his theology?
6. There have been efforts to harmonize the statement with Luther's actual written corpus. LW 54 suggests the comment can be harmonized with Luther's sermon from 1536 in which he asserted that "Christ was reproached by the world as a glutton, a winebibber, and even an adulterer" (LW 54:154, fn. 100). Lutheran theologian Arthur Carl Piepkorn compares the statement to Luther's theological motif that Christ became sin for us.
7. There is ample meaningful textual evidence Luther held to the divinity of Christ. If Roman Catholics are using this context-less quote, remind them of Luther's repeatedly referring to Mary as "the mother of God." See also Lutheran theologian Arthur Carl Piepkorn's article documenting Luther's adherence to the divinity of Christ as well as the perfect humanity of Jesus and his sinlessness. If Luther really believed that Jesus Christ, the Son of God, committed sin, the burden of historical proof is on those making the charge.
Conclusion
Consider what Rome's defenders are asking you to believe with this quote: a verbal statement from Luther scribbled down on a piece of paper sometime between 1531 - 1532 (by a person not much is known about), an outrageous statement lacking a context, which then lay dormant in a handwritten notebook until at least 1551 or 1557, then copied by one person, then not published until approximately 350 years later, and then when it was published it is not certain what the text actually originally said... trumps all of Luther's actual verifiable writings on the nature and person of Jesus Christ... and proves Luther held that Christ committed adultery.
Unfortunately, it's quite possible none of these historical seven points will have any effect on someone using this quote to denigrate either Luther or the Reformation. For their talk about going "deep into history," some of Rome's defenders have little interest in actually doing the hard work involved with accurately and fairly studying history. The ironic aspect of this, in my opinion, is there's plenty of Luther quotes available to scrutinize that can be attributed to Luther without question. If someone is going to beat up Luther, why not use something with a better pedigree? Why resort to a second-hand comment with poor historical documentation?
Addendum
I did interact with the defender of Rome on Facebook that posted this quote. Along with getting his personal conversion story, here were some of his responses:
"... it is eye witness Testimonies of friends, students and contemporaries.....as valid as the eye witness testimonies of the Apostles etc!!!"
"yep.....dismiss eye witness testimonies of those at his table who wrote it diwn and later published it....dismiss eye witnesses of Christ as well. So I guess his eye witnesses (Lutheran Family, Friends and Students at his Table Talks are all Liars) who took notes and spoke first hand with him in private are decievers who published garbage about him....OK....BS."
"Modern Conservative Lutherans know they can't change the 16th century printed eye witness testimonies of his co-religious contemporaries so they have in the 20th century tried to rehabilitate their blessed Apostle and Prophet Founder..."
"You choke, balk and dismiss. Too funny. You got nothing."
" You love the Bible and Calvin's Systematic Theology and Studies as your guide to understand that very Bible......You have your own dead 16th Century Geneva Jack Chick as your spirit Guide...not the Bible Alone. I hope you use the Geneva Bible too.."