Why would a company use a form of long-term debt to capitalize operations versus issuing equity?

There are a lot of possible reasons.  The corporate finance experts will talk about the cost of debt versus equity, the dilution of ownership that will occur if shares are issued and the cashflow pressure that debt brings.  And many other relevant factors.  All of these are true.

However....

There are two other things which are much more important.  One is the relative condition of the debt and equity markets at the time the company needs the money.  What is the fastest, easiest and cheapest (in the sense of the cost of making the issue, not the long term cost of the finance itself) way of raising the money?

The other - which is the most important of the lot - is the personal prejudice of the CEO or finance director.  Some hate debt.  Some hate equity. 

Oh, and don't forget the banks that advise on, run or underwrite the issue: their advice may or may not be influenced by which is better for them.

The reason that The cost of debt is lower than the cost of equity because interest is Tax deductible.