Negotiating the price can be tough, so it often pays to be flexible with your stance and accept a price lower than you initially asked for.
HOWEVER, I don’t think there’s ever a good reason to volunteer discounts, as in – be the first person in the conversation who suggests it.
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Accepting a discount as a counter-offer, in exchange for other considerations, yes.
Being the one who suggests it – no._
In my experience, a volunteered discount is never really seen by the client as just a reduction in price. They’re seen as price insecurity. It will look like you are desperate or not sure what your work is worth, so you gave an offer and then immediately countered it with a lower, worse one.
“Who started it” may seem like an insignificant question, but in this case, it’s not. Again, if the client suggests a compromise and offers something in return, and we accept, that’s fine.
A volunteered discount won’t be seen as a compromise but as an actual starting point of the negotiation, and a “red flag”. One proof of that is what usually happens next – the client often asks for an even deeper discount! When the price is presented as something inherently debatable, it’s no surprise that the clients start treating it as such.
To avoid this, when presenting your price – state your initial offer and stand your ground until you get something of value in return for giving a discount.