TL;DR: Prefer quotation to summarization, and prefer longer quotations to shorter, to avoid mispresenting your sources, and to make it easy for readers to evaluate your argument.
Risks of summarization
When you use a source to support your argument, there are three approaches:
Summarize how the source supports your argument in your own words.
Summarize how the source supports your argument using a mixture of your own words and short inline quotations.
Quote the relevant parts of the source and, separately, explain in your own words how they support your argument.
The first two of these approaches come with the risk that, because the evidence is mixed with your interpretation of the evidence, the reader might confuse the two, and so get a misleading impression of how strong the evidence is. Or, worse, you might be tempted to word your summary so as to give a misleading impression because it better suits your argument.
Here are three examples of these pitfalls, based on questions here at Literature Stack Exchange:
When historians like David Hume retold the story of King Cnut and the tide, they mixed their summaries of the source (a brief 12th-century account by Henry of Huntingdon) with their guesses or deductions about the king’s motive. This created a version of events in which Cnut was trying to rebuke his flatting courtiers, something that does not appear in the source.
William Quillian summarized Richard Ellman as saying “that [James] Joyce considered Shakespeare a ‘second-rate’ playwright (after Ibsen) and Hamlet a ‘rude and barbarous’ play (à la Voltaire)”, giving the impression that the quoted phrases came from Ellmann or maybe even from Joyce as quoted by Ellmann, but in fact neither phrase appears in Ellmann, and both are misleading summarizations.
Paul Fry misleadingly summarized Jerome McGann’s argument about the textual history of Keats’ poem ‘La Belle Dame Sans Merci’, claiming that McGann wanted “to infuse Keats’s text with a pleasing political correctness” and that McGann argued that the 1820 version was suppressed by a “historical conspiracy”, claims that do not appear in McGann.
I am inclined to believe that the Hume and Quillian cases were accidental distortions, but in Fry’s case it seems likely that he succumbed to temptation.
Summarizing your sources instead of quoting them requires the reader to take your summary on trust. Someone who wants to check your work has to get hold of your source, which is likely to be difficult and expensive if they don’t have access to a university library, and tedious and time-consuming even if they do. This is why the temptation to distort your summary arises: because you know that it is unlikely that anyone will check up on you.
To avoid these risks, I recommend that you prefer quotation to summary where possible. It won’t always be possible, because the relevant part of the source might be too long to quote in full, but even in these cases you should try to supplement your summary with a quotation of your source’s key point or conclusion. This makes it easier for readers to check your argument, and helps keep you honest.
The conventional advice
So why, given these risks, does writing advice often recommend summarization over quotation? I think this is because the advice is usually offered to two groups of writers:
Students, because the purpose of writing essays is to demonstrate your command of the material, which you do by putting it in your own words. The risk of misleading summary is low, because the intended readership is the instructor, who ought to know the material well enough to identify and correct the student’s mistakes.
Scholars, because the purpose of writing articles is to make an original contribution, which necessarily has to be in one’s own words; because the readership consists of other scholars who can be presumed to have the skills to follow your references, and the necessary access to books and journals via university libraries; and because when articles were printed on paper, it was important to economize on space, and this continues as a tradition even though this economy is no longer necessary.
Here at Literature Stack Exchange we are not in either of these cases. We are not trying to demonstrate our command of a subject to an instructor, nor make an original contribution to scholarship; we are not a community of scholars whose claims can be presumed trustworthy; and we are writing for a general readership who may not all have the skills to follow references, nor the necessary access to university libraries.