Why are men more susceptible to severe COVID-19?
Update -- In the time since this question was asked, two relevant articles have been published, one in Nature Reviews Immunology and one in medRxiv (note: medRxiv is a preprint server and is therefore not peer reiewed).
Scully, E.P., Haverfield, J., Ursin, R.L. et al. Considering how biological sex impacts immune responses and COVID-19 outcomes. Nat Rev Immunol (2020).
Takahashi, T., Wong, P., Ellingson, M., et al. Sex differences in immune responses to SARS-CoV-2 that underlie disease outcomes. medRxiv (2020).
Besides the genetic factors related to viral entry that I've explained below, these papers explain the immunological factors that may determine the higher susceptibility of males to severe SARS-CoV-2 infection, including sex-specific differences in early antiviral response, innate immune repsonse, and adaptive immune response.  Figure 2 of Scully et al. provides a graphic summary.

Genetic factors
SARS-CoV-2 entry into human cells is thought to depend on two human proteins:

ACE2 -- a transmembrane protein important for blood pressure control.1  The viral spike protein binds the enzymatic domain of ACE2, facilitating translocation of the virus into the cell.2
TMPRSS2 -- a serine protease with a transmembrane domain.  The proteolytic activity of this enzyme is thought to play a role in &quot;priming&quot; the viral spike protein.3

So, a place to start would be to ask if there are sex-specific differences in the expression or localization of these proteins.
ACE2
No significant differences in lung ACE2 activity have been found between male and female mice.4  In rats, however, lung ACE2 levels are reduced with aging in both males and females, with significantly higher ACE2 expression in old female rats compared to old males.5 Assuming that rats are a good model for sex-specific human lung protein expression, this observation counters the simple explanation that men are more likely to have severe COVID-19 due to higher ACE2 expression.
A recent preprint 6 presents an interesting hypothesis -- that ACE2 mosaicism due to X inactivation may be protective against SARS-CoV-2 in women.
From the abstract:

The fact that the human ACE2 protein is encoded on the X chromosome means that males who carry rare ACE2 coding variants will express those variants in all ACE2-expressing cells, whereas females will typically express those variants in a mosaic distribution determined by early X-inactivation events.

So, since males are hemizygous for the X-chromosome, males that have an ACE2 variant that binds strongly to the SARS-CoV-2 spike protein will only express that variant in their lungs.  Females have two X-chromosomes, though only one is expressed in any given cell due to X-inactivation.  If a female is heterozygous at the ACE2 locus, with one allele that encodes a protein that strongly binds SARS-CoV-2 spike protein and one allele that encodes a protein that weakly binds SARS-CoV-2 spike protein, mosaic expression of the maternal and paternal alleles may give partial protection from infection.
The authors found that ACE2 is generally intolerant of loss-of-function variants, though many missense variants occur at and near residues predicted to bind SARS-CoV-2.  Such variants were detected at a rate of 3.9 males per 1000 and 8.5 females per 1000.  However, the most popular missense variant, rs41303171, does not lie in a domain of ACE2 that is predicted to interact with SARS-CoV-2.  Additionally, this SNP is only observed in 1.7% of male and 3.1% of female samples, so it is not obvious that this explanation can account for the sex-specific discrepancy in severe COVID-19 at the population level.
TMPRSS2
Currently, evidence suggests that there are no sex-specific differences in TMPRSS2 expression in the lungs of humans or mice.7  Note, however, that only transcript levels have been evaluated in this context, and that TMPRSS2 activity would need to be evaluated to determine that proteolytic action is not different between sexes.

Non-genetic factors
Worldwide, men smoke five times as much as women.8
Smoking is co-morbid with severe COVID-19 9, likely due to decreased lung capacity, though possibly through a mechanism involving increased TMPRSS2 expression.7  From the same TMPRSS2 paper cited above:

regardless of sex, smoking significantly increases the expression of TMPRSS2, which reverts back to never-smoker levels in former smokers

Indeed, one recent study of more than 1,000 COVID-19 patients reported greater than two-fold increased risk for intensive care unit admission and death in smokers as compared with non-smokers.10
There may be cultural factors affecting disease progression, as well.  If men are less likely to wear masks or follow other guidelines to reduce the risk of infection, then infected men may be exposed to a higher infectious dose than women. Initial infectious dose may be positively correlated with viral load 11, and higher viral load is associated with a more severe prognosis for SARS infections.12
It could simply be the case that symptomatic men are less likely to be tested (a &quot;tough it out&quot; mentality), and therefore would be less likely to receive treatment that prevents a mild infection from becoming severe.

Citations

A Novel Angiotensin-Converting Enzyme–Related Carboxypeptidase (ACE2) Converts Angiotensin I to Angiotensin 1-9
SARS coronavirus entry into host cells through a novel clathrin- and caveolae-independent endocytic pathway
Activation of the SARS coronavirus spike protein via sequential proteolytic cleavage at two distinct sites
Sex differences in renal angiotensin converting enzyme 2 (ACE2) activity are 17β-oestradiol-dependent and sex chromosome-independent
Age- and gender-related difference of ACE2 expression in rat lung
ACE 2 Coding Variants: A Potential X-linked Risk Factor for COVID-19 Disease
No evidence that androgen regulation of pulmonary TMPRSS2 explains sex-discordant COVID-19 outcomes
Gender empowerment and female-to-male smoking prevalence ratios
COVID-19 and smoking: A systematic review of the evidence
Clinical Characteristics of Coronavirus Disease 2019 in China
SARS-CoV-2 viral load and the severity of COVID-19
Initial viral load and the outcomes of SARS