Why doesn't HDL cause diseases like LDL?
Thank you for the fascinating question! It was tough to research but very worthwhile.

LDL is actually not such a bad molecule. It is formed from VLDL/IDL after VLDL/IDL distribute triglycerides, phospholipids, cholesterol and cholesterol esters to peripheral cells. With less to give, LDL subsequently tries to be helpful by providing any needy peripheral cell with leftover cholesterol necessary for plasma membrane synthesis and other cellular functions. In fact, even endothelial cells, which line the vasculature, have LDL receptors to welcome any cholesterol packages from LDL. Another function of LDL is to make HDL even ‘healthier’ by removing cholesteryl ester from HDL molecules in the periphery and returning it to the liver. 

Remember that LDL does not contain exactly the same components as its precursors. LDL does not have the ApoE &amp; C proteins that VLDL and IDL have. LDL has only ApoB-100 and a concentrated level of cholesterol. LDL-family receptors generally recognize ApoE and ApoB, which are located on VLDL and IDL, thus easily pulling them into the liver out of the bloodstream, via endocytosis. Because LDL contains only the ApoB protein, it is less easily recognized. Thus, more LDL lingers in the blood. This is supported by the lengths of their half-lives--- with VLDL and IDL half-lives being about 6 hours and LDL half-life being about 3 days. 



Where disease comes in is with an imbalance of fat in our diet. This is explained in detail by this extensive article on Managing Dyslipidemia: The Triglyceride/High-Density Lipoprotein Axis. The article explains that disease cannot solely be blamed on LDL alone. A high fat diet leads to elevated triglycerides in the blood stream, which increases blood viscosity, interference with endothelial function, stimulation of arterial inflammation, and interference with normal blood coagulation. These conditions can predispose to atherosclerotic lesions. In addition, there is an up-regulation of protein ApoC-III, which subsequently increases the half-lives of VLDL and IDL particles. It even increases the activity of an enzyme called cholesteryl ester transfer protein (CETP), which can exchange cholesteryl ester in HDL and LDL for triglycerides in VLDL and IDL, and vice versa. This leads to change in composition of HDL and LDL, making them more triglyceride-rich, physically smaller, and less interactive with their respective membrane receptors. With HDL even smaller, it is also easily filtered through the kidneys, leading to lower levels. All this means there is more circulating LDL in the blood. 

LDL enters the endothelium via breaks in the endothelial wall created naturally (by dying or dividing cells) or through injury (by inflammatory processes including infections, chemical exposures) or it leaks in through junctions between endothelial cells when there is high intraluminal pressure (such as in hypertension). From there, LDL can become oxidized and ingested by macrophages, forming foam cells, which can rupture spewing its contents into the surrounding arterial wall, leading to the beginning of atherosclerotic lesion. 

Why can’t HDL cross through endothelial wall, too? Actually, it can! According to the above-mentioned article, “HDL particles [in its native form] appear to have the potential to delipidate cholesterol from foam cells” at the site of a lesion. With HDL being smaller, it can enter the endothelium to interact with foam cells. Its interaction, however, is the opposite of LDL. Cholesterol is transferred back from the foam cell to HDL, reversing the oxidized LDL-induced process. In addition, “HDL protects LDL from oxidation by [using] metal ions” before oxidized LDL can lead to further damage. This mechanism is still unknown. 

Why can’t HDL become oxidized, too? Indeed, this can also happen! However, it appears again than oxidized HDL behaves oppositely to oxidized LDL. “Oxidative tyrosylation of high density lipoprotein by peroxidase enhances cholesterol removal from cultured fibroblasts and macrophage foam cells [5].” There is a caveat though. This function seems to depend on how HDL is oxidized. If oxidized by copper or hypochlorous acid, HDL “loses its ability to remove cholesterol from cultured cells [6].” 

In short, given the very same conditions including oxidative environment and entry into the endothelial cell, HDL inherently behaves oppositely to LDL. This likely is related to their inherently different composition, but we have yet to understand how this occurs at a molecular level. However, HDL could technically be 'bad' under the right oxidative conditions. In the end, LDL is given a bad reputation because its relatives IDL/VLDL easily escape into other cells via receptors and HDL concentration is lowered partially by renal filtration. 

References: 


Mera, Steven L. Understanding Disease: Pathology and Prevention. 
http://www.ncbi.nlm.nih.gov/pubmed/19592615
http://www.nature.com/nrmicro/journal/v8/n2/fig_tab/nrmicro2269_F1.html
Libby, P (2006). "Inflammation and cardiovascular disease mechanisms". American Journal of Clinical Nutrition. 83(suppl) (2): 456S–460S. 994471841.
http://www.medscape.org/viewarticle/582014
http://atvb.ahajournals.org/content/23/9/1488.full#ref-16