Is the labor force participation rate related more to labour supply or to labour demand? Or both? I have read several Labor Economics books, but I am stuck. Is the labor force participation rate related more to the labour supply or to the labour demand? 

If the labor force participation rate decreases in a year (with respect to the previous year), should we worry that employers are not hiring (i.e., labor demand)? Or, is it due to workers that are not currently interested in work (i.e., homemakers)?

Furthermore, from this and this online documents it seems that the LFPR (labor force participation rate) is strongly dependent on labor demand from employers (i.e., positive/negative business cycles) rather than from labor supply. For instance, the LFPR dropped strongly during the Great Recession as employers were not willing to hire workers. Any opinion on these problems?
Traditionally, labor force participation is best thought of as a supply-side phenomena. That is, a certain subset of our nation's population is jobless but is jobless by choice. For example, consider a stay-at-home parent. So, we have agents making a decision to not supply labor. 

However, there is a hint of the demand side at play here. For example, a very weak demand side might discourage workers, thereby compelling the marginal participant to exit the labor force.  

So, to be explicit: LFP is a supply-side concept. However, there is a mechanism through which demand side forces can factor into LFP.