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Photograph made by Max Alpert shows a dead boy holding a pigeon. It seems that the child has been tortured before he was killed.

Source: Federal Archive Agency of Russia, Russian state archive of photographic and movie documents, item nr. 0-259138 (Российский государственный архив кинофотодокументов, aрхивный номер: 0-259138)

According to Russian Wikipedia the name of this boy was Victor Ivanovich Cherevichkin and the Germans killed him because he did not kill his pigeons. After they occupied Rostov-on-Don (the hometown of this boy), the issued an order that made illegal to own pet pigeons.

The boy hid his pigeons at home and was killed for that by the Germans.

Why did the Germans not allow people to own pigeons? What made the possession of pigeons so dangerous that it justified the killing of a child?

Update 1 (2019-04-07 00:09 CET): Here is the Original text from Russian Wikipedia article:

22 ноября 1941 года был издан приказ об уничтожении голубей в районах города Ростова. Вопреки предписанию немецкого командования об уничтожении принадлежащих местному населению домашних голубей, подросток в течение недели скрывал имевшихся у него птиц.

28 ноября 1941 года немцы застали Виктора Черевичкина выпускающим нескольких голубей у здания, в котором размещался штаб, и обнаружили в сарае во дворе его дома голубятню.

The Germans were concerned that carrier pigeons would be used to communicate with Soviet forces. Carrier pigeons were used extensively during both World Wars.

From the Rostov-on-Don tourism website:

Черевичкин Виктор Иванович (1925–1941) – ростовский пионер-герой.
Когда немцы в 1941 году взяли Ростов-на-Дону, они приказали городским владельцам голубятен уничтожить всех своих птиц. Гитлеровцы опасались, что с помощью почтовых голубей ростовчане будут передавать советским войскам разведывательную информацию.
Но Витя не подчинился приказу и тайно продолжал держать голубей, с их помощью наладив связь с партизанами. Но был «раскрыт» и арестован. Перед тем, как его увели на казнь, Витя успел выпустить всех голубей на волю.
На Нюрнбергском процессе фото убитого мальчика с голубем в руках было представлено в числе документов, обличающих фашизм.
В 1954 году был включен в официальный список пионеров-героев, выпущенного в составе Книги почета Всесоюзной пионерской организации им. В.И. Ленина.

(English translation)

Cherevichkin Viktor Ivanovich (1925-1941) - Rostov pioneer-hero. When the Germans in 1941, took Rostov-on-Don, they ordered the town pigeon owners to destroy all their birds. The Germans feared that using carrier pigeons Rostov will send intelligence information to the Soviet troops. But Victor did not obey the order and secretly continued to keep pigeons, with their help he established the connection with the guerrillas. But he was "discovered" and arrested. Before he was led away to death, Victor managed to release all the pigeons loose. At the Nuremberg trial a photo of a murdered boy with a dove in his hands was represented among all the documents denouncing fascism. In 1954 he was included in the official list of the pioneer heroes, released as part of the Book of Honor All-Union Pioneer Organization of V.I. Lenin.

• (my emhpasis)

I haven't (yet) found an English translation of the "official list of the pioneer heroes, released as part of the Book of Honor All-Union Pioneer Organization of V.I. Lenin", but I suspect that you'll find more detail there.

The pigeons could have been homing pigeons, used to carry information from spies in Rostov-on-Don back to Soviet-controlled territory. Banning pigeon-keeping in occupied territory was fairly normal for the time; murdering children for disobeying the occupier's decrees was sadly normal for Nazi-occupied territory.

There's a lot of information about homing pigeons in wartime in the book Secret Pigeon Service: Operation Columba, Resistance and the Struggle to Liberate Europe by Gordon Corera, published by Collins in 2018.