Why is cost of equity considered to be higher than debt ?

There are virtually no tax benefits to equity, where debt is tax-deductible.

Equity holders share in profits and have a high expectation for a decent return, putting the value of your company at risk much more so than straight debt does. Debt holders do not share their profits with the debtors.

Debt can be paid off and goes away, equity holders tend to be forever... or close to it.