Why people use ‘Tsumori’ when excusing?

You have leaned ‘ Tsumori’ which describes your plans in the textbook.

8時に　学校に行くつもり　です

I am planning to go to school at 8.

あしたは　仕事しないつもりです

I am planning not to do my work tomorrow.

How about the past tense? The sentence means you had the another actions in spite of your original plans. Which means you didn’t execute the one you had originally planed, for example…

8時に　学校に行くつもり　でした。でも、実際には 9時に　到着しました。

I was planning to go to school at 8 but actually I have arrived at 9.

仕事しないつもり　でしたが、結局　会社のメールをチェックしてしまった。

I was planning not to work but eventually I have checked the company’s emails.

No matter it is present or past tense, above examples mean about the plans.

***I want you to note is that ‘ tsumori’ is used only for your own plans, not for others. In that case, please use 予定(yotei) instead.***

Now the captioned question, if you use 「あります or ありません」after 「つもり」、the meaning turns different?

Yes, which is about the intention.

彼女を誘うつもり　は　ありません。

I have no intentions to invite her.

あした　仕事するつもり　は　ありません

I have no intentions to do a job tomorrow.

‘Tsumori’ covers a very wide meanings in Japanese.

Do you know the song’ Jelous Guy’?

In lyrics, there is a word such as ‘ I didn’t mean to hurt you’.

it would be translated「ごめんよ、君をきずつけるつもりは　なかったんだ」in Japanese.

We can tell John Lennon didn’t mean, didn’t have intentions to hurt Yoko from that words.