Explain why its necessary, most people will understand, but if they fight it, invite a counter offer.

In the Chicago area, however, it is very likely you'll wait four months to get a counter offer from the bank, so I always tell my investors, expect to negotiate.  

6 days ago I entered in to a contract with a seller, my contract has a inspection contingency and a counteroffer contingency, I am well within my 10 day due diligence period and I have decided to exercise my inspection clause after my partner pointed several concerns a counteroffer was also made and the seller turned it down, I emailed him with a written notice of cancellation, I went to the title company and they basically said that he has to give his  approval to refund my EM, now the guy is dragging his feet and doesn't answer his phone when I call, and the title company says that their attorney has to look over the contract and decided how my EM should be disbursed!

They may not take the offer as originally written but they will probably give you a counter offer.  

What he then did, was proposed a new agreement, and you counter-offered with a new lease agreement.  

Our house has an updated kitchen with granite and updated appliances, I'm thinking is worth $360 to $370+.My RE agent said we could give a counter offer, is this normal in any scenario? 

There was a counter offer made and there was one check mark changed that the seller did not notice. 

After the inspection, that uncovered a lot of major problems, I counteroffered a new fair price. 

While I used an agent who surely did a lot of work with the offers/counter offers, I wonder how much could be saved by learning those things and DIYing it.

After the heated back and forth one of the agents said “counter offers are coming out soon and it’ll be 1.125 mil.