Why does the left have a bad record and a bad reputation with regard to its attachment to democracy? I need to refine the question and provide some context for it, otherwise I'll be taken to be asking and/or saying something I'm not.
So, first, it's not the whole left to which the question applies but only a part of it. There is a democratic left whose commitments in this regard are clear. Second, there is so obvious an answer to the bald question as I've posed it that some might wonder why I've bothered: Stalinism, the Gulag, the political record of all those countries that have embarked on an anti-capitalist path. Where's the puzzle that prompts my question? To give the context that explains my asking it I need to say a bit more. For the left I'm talking about is not the old Stalinist left, compromised by the lies it told and the excuses it made for the 'great socialist experiment' of the USSR and its crimes; it's the left of a later generation, the one I grew up in, which claimed to know the lessons of that history and for whom socialist democracy was a regularly and, I think, mostly sincerely emphasized commitment (see related remarks by me here and here).
Under these specifications then, why? A complete answer must probably have several parts to it, but here's one part I'd like to propose. It arises from the combination of political impulses harboured by a certain kind of Western leftist when responding to (a) the undemocratic practices of would-be socialist or anti-imperialist or (in some assumed sense) 'progressive' states, and (b) claims made for the democracies of the wealthier capitalist countries.
Three things mark this combination of responses. (i) A temptation to look for mitigating considerations or to make excuses - take your pick - for the lack of democracy in the (a)-type countries: blockade, encirclement, underdevelopment, legacy of colonialism etc. (ii) An attempt to point to features compensating for a lack of democracy: social and economic achievements of one kind and another. (iii) Claims that, in any case, the democracies of advanced capitalist societies are either flawed and limited as democracies or not really democracies at all but disguised forms of dictatorship.
We approach what is the crux of the matter. It is not that there is nothing at all to be said for the above three tropes. A country mired in poverty has fewer democratic resources than a wealthy one; where there are achievements to note, there's nothing wrong with noting them; the democracies of the capitalist world are indeed flawed in certain ways - differently, and some more than others, but invariably not offering all their citizens an equality of influence and rights.
Nonetheless, there is a central piece of bad faith in the way that these three themes typically combine on the left to enable their partisans to evade a single inescapable fact: namely that, flawed as they may be, the capitalist democracies are democracies and none of the would-be anti-capitalist countries, anywhere, has managed to sustain comparably good or better democratic institutions over any length of time. Note that I do not say this means it could never happen; I don't believe that. What it does mean, however, is that the democratic institutions we are familiar with have yet to be improved upon in any of those places that some leftists are given to casting an indulgent eye upon even while they seek to distance themselves critically from the institutions they themselves benefit from and which are superior.
Unwilling to profess a clear allegiance towards what is democratically better, a certain type of leftist is always ready to make allowances for what is democratically worse. Is it any wonder, then, if his or her democratic avowals are regarded by many with suspicion?