What is the main challenge in creating a chemical male contraceptive?
I am going to summarize a few reasons for both why contraception is "easier" for women, and for why it is "harder" for men. They are both biological and sociological. 

Easier for women

The female cycle is more complicated

The female cycle leading to ovulation is regulated by several hormones that interact. As such, it is easier to disturb. 


  The system is so sensitive that even the slightest alteration in any of these factors can disrupt its fluidity and lead to anovulation


(Anovulation = a cycle where no ovulation occurs) Source: Anovulation: Background, Pathophysiology, Epidemiology

Even in young women, this occurs naturally. 


  Estimates of chronic anovulation rates range from 6-15% of women during the reproductive years


Female bodies l already have a "built-in mechanism for contraception

As ovulation needs to be suppressed during pregnancy, there is already a mechanism in place by which this can happen. 

Women are more affected by pregnancy

Since women are more affected by pregnancy and childbirth, the risk they feel they have when they don't use contraception or use it incorrectly is larger. 

Contraceptives for women have more than one use


  More than half of pill users, 58%, rely on the method at least in part for purposes other than pregnancy prevention. Thirty-one percent use it for cramps or menstrual pain, 28% for menstrual regulation, 14% for acne, 4% for endometriosis, and 11% for other unspecified reasons. 


Beyond Birth Control: The Overlooked Benefits of Oral Contraceptive Pills

Harder in men

It only takes one

While the saying "it only takes one sperm"  is probably an exaggeration, it carries a certain truth - you really need to shut down the production of sperm or the risk of a pregnancy is too high. Both the pill and the various IUD options have set a high bar for what's considered an acceptable risk. 

Side effects and effectiveness

While hormonal contraception for women already has a multitude of side effects, often unrelated to the reproductive system, this is certainly not easier in men. The most prohibiting side effect encountered so far is impotence - not much use in taking birth control to have sex without risk of pregnancy when doing so leads to no sex at all. 


  Progestins have been used in multiple small studies of men for suppression of spermatogenesis and testosterone production. Progestins used alone result in significant side effects such as loss of libido and erectile dysfunction. 


Update on Male Hormonal Contraception: Is the Vasectomy in Jeopardy?

(Decreased libido is also a side effect in female hormonal contraception, though. The reasons why it's seen as more acceptable there are probably sociological) 

That review is a good overview on what has been tried until 2010. Many solutions failed because of side effects or because they didn't work well enough. 

On testosterone:


  Of note, this international study revealed that 91% of Asian and 60% of Caucasian patients became azoospermic, suggesting an ethnic difference in endocrine response


Testosterone proved to be rather good in other doses and combinations, but is not that easy to handle because it requires injections and can't be taken orally. 


  Testosterone alone has side effects, including acne and oily skin, mood changes, increased hemoglobin and hematocrit, weight gain, decrease in testicular volume, sleep apnea, gynecomastia and possible effects on cholesterol. There are no long-term data with testosterone use and normal men regarding prostate symptoms, growth or cancer. In an era of fear of using medications on relatively healthy individuals, acceptability of routine use may be a major concern, given recent data on medical treatment of menopause with estrogen/progestin therapy. In addition, anabolic steroids are a controlled substance and regulation of this industry is very strict at this time. Abuse of these drugs could easily become prevalent with its widespread use and availability for contraception.


On cryproterone acetate:


  Doses ranging from 25 to 100 mg per day have suppressed spermatogenesis, but side effects have precluded subsequent studies. 


And so on... 

The market factor

A side effect of the contraceptive options for women being so well-accepted, women often feeling responsible for contraception and also using hormonal contraception anyway, for reasons unrelated to pregnancy, is that the market for male contraception is not that easy and pharmaceutical companies have been pulling away from it. Especially in light of the research difficulties. 


  Although Bayer, Wyeth and Organon were once active in research and development of a male method, all three discontinued their programs between 2005 and 2008 although the industry continues to actively pursue programs for hormonal contraception and hormonal-replacement therapy for women. In withdrawing support, company representatives cited corporate changes in direction and the perception that safety standards demanded by regulatory bodies would require such extensive evidence as to make further research financially infeasible


Current challenges in male contraceptive research

This is not to say that there really is no market. As you mentioned in the comments, at least in questionnaires, many men say they would use male hormonal contraception and many women say they would like their partners to use it. See, for example, Market size for male contraception (plus the following pages of that paper) 

But you asked about the challenges ;-)

I think it's also interesting to note that the search for hormonal contraception started for both men and women. It's just that the "solution" was found for women first and then got popular really fast.