Do not declare yourselves pure

Those who avoid the major sins and immoralities, only [committing] slight ones. Indeed, your Lord is vast in forgiveness. He was most knowing of you when He produced you from the earth and when you were fetuses in the wombs of your mothers. So do not claim yourselves to be pure; He is most knowing of who fears Him.

[Qur'aan 53:32 - Translation by Sahih International]

الذين يجتنبون كبائر الإثم والفواحش هذا نعت للمحسنين ; أي هم لا يرتكبون كبائر الإثم وهو الشرك ; لأنه أكبر الآثام

"Those who avoid the major sins and immoralities" describes the muHsiniin, meaning that they do not indulge in the major sins. And the biggest of all sins is al-shirk [to associate partners with Allaah].

فقال أبو هريرة وابن عباس والشعبي : اللمم كل ما دون الزنى

It has been attributed to Abu Hurairah and Ibn Abbbaas [by al-Qurtubi in his Tafsiir] that al-lamam [translated as slight ones in the above translation] refers to sins which are less than zinaah.

فلا تزكوا أنفسكم أي لا تمدحوها ولا تثنوا عليها ، فإنه أبعد من الرياء وأقرب إلى الخشوع

So do not claim yourselves to be pure meaning that do not praise yourselves because [not praising oneself] is closer to humility and far away from showing off.

Reference(s):

al-Jaami li ahkaam al-Qur'aan also known as Tafsiir al-Qurtubi