Cooked white asparagus is stringy
Contrary to popular belief, older asparagus is not what causes larger stalks and larger stalks are not tougher than thin stalks. The size of the stalk is determined by the variety of asparagus.

As cited in this article in the  NYTimes , asparagus will start to get tough immediately upon cutting. It starts to toughen at the bottom and continues up the stalk. The asparagus need to be chilled very soon after cutting to prevent this.


  Most of this loss of sweetness and toughening happens in the first day after harvest. Farmers can minimize it by chilling new-cut asparagus right away. But a delay of just four hours between harvest and chilling causes the spears to toughen significantly. So does allowing the chilled spears to warm up to 60 degrees or more in a grocery display or at the farmers’ market.


So, in short the toughness is most likely caused by improper storage when the asparagus is harvested.

We have two asparagus beds and we chose a large stalk variety as it seemed to have a little more flavor (to us). Once or twice we have let the stalks grow to over 2' long and they were still tender. That said, when we cut them, they are immediately refrigerated and stay chilled until we cook them.